Differential Equations

CBSE Class 12 Mathematics · 113 board questions from this chapter; 112 listed below, 2022–2026

• The general solution of the differential equation x dy-y d x=0 is2026
• The order and degree of the differential equation: d/(d x)( sin y)=y^2 respectively are2026
• The integrating factor of differential equation R (d x)/dy+P x=Q where P, Q, R are functions of y is2026
• The general solution of the differential equation dy/dx=(√y)/(√x) is2026
• Product of the order and degree of differential equation 1+(dy/dx)^3=λ((d^3 y)/(dx^3))^2 is:2026
• The integrating factor of the differential equation 2 x dy/dx-y=3 is2026
• The sum of the order and the degree of the differential equation y=x dy/dx+3[2-(dy/dx)^2] is:2026
• The sum of the order and the degree of the differential equation 4[(d^2 y)/(dx^2)]^2+3[1+(dy/dx)^2-y]=0 is:2026
• The order and degree of the differential equation d/(dx)(e^y)=0 respectively are2026
• The order and degree of the differential equation 1+((d^3 y)/(dx^3))^3=λ (d^2 y)/(dx^2) is:2026
• The order and degree of differential equation y=((d^2 y)/(dx^2))^2-λ dy/dx is:2026
• Which of the following is not a Linear Differential Equation?2026
• (d y)/(d x)=F(x, y) will be a homogeneous differential equation for which of the following functions? (i) F(x, y)=3 x+2 y (ii)…2026
• The order and degree of differential equation (d^2 y)/(dx^2)=1-((d^3 y)/(dx^3))^2 is:2026
• The general solution for the differential equation (d y)/(d x)=e^3 x-y is:2026
• The general solution of the differential equation: x^2 dy+y^2 d x=0 is2026
• The order and degree of the differential equation: d/(d x)(y^′)^3+(y^′)^3=1 respectively are where y^′=dy/dx2026
• Assertion: One of the particular solutions of the differential equation (d y)/(d x)=e^x+y can be e^x+e^-y=-2. Reason (R):…2026
• Find the general solution of the differential equation: y^2 d x+(x^2-x y+y^2) dy=0 OR Find the particular solution of the…2026
• Find the general solution of the differential equation (x^2+y^2) d y=x y d x. OR Find the particular solution of the differential…2026
• Solve the differential equation (x- sin y) d y+ tan y d x=0.2026
• Solve the differential equation (x+2 y^3) d y=y d x.2026
• Solve the differential equation y dx+(x-y^3) dy=0.2026
• Find the general solution of the following differential equation: x^2 dy/dx=x^2+x y+y^2 OR Find the particular solution of the…2026
• Find the general solution of the differential equation 2 x^2 dy/dx=y^2+2 xy. OR Find a particular solution of the differential…2026
• Solve the following differential equation: x dy/(d x)=y-x sin^2(y/x), given that y(1)=(π)/6 OR Find the general solution of the…2026
• Find the general solution of the differential equation (y^2-x^2) d x=2 x y dy OR Find the particular solution of the differential…2026
• Find the general solution of the differential equation (x^2-y^2) d x+2 x y d y=0 OR Solve the differential equation sin x cos y d…2026
• Solve the differential equation y e^y dx=(y^3+2 x e^y) dy, when y(0)=1. OR Find the general solution of the differential equation…2026
• The integrating factor of differential equation (x+2 y^3) (d y)/(d x)=2 y is2025
• The order and degree of the differential equation (d^2 y)/(d x^2)+4((d y)/(d x))=x log ((d^2 y)/(d x^2)) are respectively:2025
• The order and degree of the differential equation [(d^2 y)/(d x^2)-1]^2=(d y)/(d x) are, respectively:2025
• The order and degree of the following differential equation are, respectively: -(d^4 y)/(d x^4)+2 e^d y / d x+y^2=02025
• The integrating factor of the differential equation dy/dx+y=(1+y)/x is2025
• The solution for the differential equation log ((d y)/(d x))=3 x+4 y is:2025
• The order and degree of differential function [1+(dy/dx)^2]^5=(d^2 y)/(d x^2) are2025
• The integrating factor of the differential equation (d x)/(d y)=(x log x)/(2/x log x-y) is:2025
• The integrating factor of the differential equation (d x)/(d y)=(-(1+ sin x))/(x+y cos x) is:2025
• The integrating factor of the differential equation ((e^-2 √x)/(√x)-y/(√x)) (d x)/(d y)=1 is:2025
• The sum of the order and degree of the differential equation [1+((d y)/(d x))^2]^3=(d^2 y)/(d x^2) is:2025
• The solution of the differential equation (d y)/(d x)=-x/y represents family of:2025
• The order and degree of the differential equation ((d^2 y)/(d x^2))^2+((d y)/(d x))^2=x sin ((d y)/(d x)) are:2025
• The integrating factor of the differential equation dy/dx+y tan x- sec x=0 is:2025
• If p and q are respectively the order and degree of the differential equation d/(d x)(dy/(d x))^3=0, then (p-q) is2025
• Solve the differential equation 2(y+3)-x y (d y)/(d x)=0; given y(1)=-2. OR Solve the following differential equation: (1+x^2) (d…2025
• Find the particular solution of the differential equation dy/dx-y/x+cosec(y/x)=0; given that y=0, when x=1.2025
• Solve the differential equation x cos (y/x) (d y)/(d x)=y cos (y/x)+x.2025
• Find the particular solution of the differential equation [x sin^2(y/x)-y] d x+x d y=0 given that y=(π)/4, when x=1.2025
• Solve the differential equation (d y)/(d x)= cos x-2 y.2025
• Solve the differential equation: x^2 y d x-(x^3+y^3) d y=0. OR Solve the differential equation (1+x^2) (d y)/(d x)+2 x y-4 x^2=0…2025
• Solve the differential equation (x^2+y^2) d x+x y d y=0, y(1)=1.2025
• Solve the differential equation (x- sin y) d y+( tan y) d x=0, given y(0)=0.2025
• Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at…2025
• During a heavy gaming session, the temperature of a student's laptop processor increases significantly. After the session, the…2025
• The number of solutions of differential equation (d y)/(d x)-y=1, given that y(0)=1, is:2024
• The solution of the differential equation (d y)/(d x)=1/(log y) is:2024
• The degree and order of differential equation y^′ ′ 2+ log (y^′)=x^5 respectively are:2024
• The integrating factor of the differential equation x (d y)/(d x)-y=x^4-3 x is:2024
• x log x (d y)/(d x)+y=2 log x is an example of a:2024
• The differential equation (d y)/(d x)=F(x, y) will not be a homogeneous differential equation, if F(x, y) is:2024
• The integrating factor of the differential equation (1-x^2) (d y)/(d x)+x y=a x, -1<x<1, is:2024
• The number of arbitrary constants in the particular solution of the differential equation log (dy/dx)=3 x+4 y; y(0)=0 is/are2024
• The integrating factor of the differential equation dy/(d x)+2/x y=0, x ≠ 0 is:2024
• The general solution of the differential equation x dy+ydx=0 is:2024
• The integrating factor of the differential equation (x+2 y^2) (d y)/(d x)=y(y>0) is:2024
• The general solution of the differential equation dy/dx=e^x+y is:2024
• The order of the differential equation (d^4 y)/(d x^4)- sin ((d^2 y)/(d x^2))=5 is:2024
• The order and degree of the differential equation [1+((d y)/(d x))^2]^3=(d^2 y)/(d x^2) respectively are:2024
• The degree of the differential equation (y^′ ′)^2+(y^′)^3=x sin (y^′) is:2024
• The order of the following differential equation (d^3 y)/(d x^3)+x(dy/(d x))^5=4 log ((d^4 y)/(d x^4)) is:2024
• Find the general solution of the differential equation (d y)/(d x)=(x^2+y^2)/(2 x y).2024
• Find the particular solution of the differential equation given by 2 x y+y^2-2 x^2 (d y)/(d x)=0; y=2, when x=1. OR Find the…2024
• Find the particular solution of the differential equation given by x^2 (d y)/(d x)-x y=x^2 cos^2(y/(2 x)), given that when x=1,…2024
• Find the particular solution of the differential equation dy/dx=y cot 2 x, given that y((π)/4)=2. OR Find the particular solution…2024
• Find the particular solution of the differential equation dy/dx-2 x y=3 x^2 e^x^2; y(0)=5 OR Solve the following differential…2024
• Solve the following differential equation: ( tan^-1 y-x) d y=(1+y^2) d x2024
• A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time. Using exponential…2024
• Degree of the differential equation sin x+ cos ((d y)/(d x))=y^2 is2023
• The integrating factor of the differential equation (1-y^2) (d x)/dy+y x=ay,(-1<y<1) is2023
• The sum of the order and the degree of the differential equation (d^2 y)/(d x^2)+((d y)/(d x))^3= sin y is:2023
• The solution of the differential equation (d x)/x+(d y)/y=0 is:2023
• What is the product of the order and degree of the differential equation (d^2 y)/(d x^2) sin y+((d y)/(d x))^3 cos y=√y?2023
• The integrating factor for solving the differential equation x (d y)/(d x)-y=2 x^2 is:2023
• The order and degree (if defined) of the differential equation, ((d^2 y)/(d x^2))^2+((d y)/(d x))^3=x sin ((d y)/(d x))…2023
• The order and the degree of the differential equation (1+3 (d y)/(d x))^2=4 (d^3 y)/(d x^3) respectively are:2023
• The number of solutions of the differential equation (d y)/(d x)=(y+1)/(x-1), when y(1)=2, is:2023
• The general solution of the differential equation x d y-(1+x^2) d x=d x is:2023
• The integrating factor for solving the differential equation x dy/dx-y=2 x^2 is:2023
• Find the general solution of the differential equation: d/(d x)(x y^2)=2 y(1+x^2) OR Solve the following differential equation: x…2023
• Find the general solution of the differential equation: (d x)/(d y)=(e^x / y(x/y-1))/(1+e^x / y). OR Find the particular solution…2023
• Find the particular solution of the differential equation dy/dx+ sec^2 x · y= tan x · sec^2 x, given that y(0)=0. OR Solve the…2023
• Find the particular solution of the differential equation dy/dx=(x+y)/x, y(1)=0. OR Find the general solution of the differential…2023
• Find the general solution of the differential equation: (d y)/(d x)-(2 y)/x= sin 1/x. OR Find the particular solution of the…2023
• Find the general solution of the differential equation: (x y-x^2) d y=y^2 d x OR Find the general solution of the differential…2023
• An equation involving derivatives of the dependent variable with respect to the independent variables is called a differential…2023
• Find the sum of the order and the degree of the differential equation: (x+dy/dx)^2=(dy/dx)^2+12022
• Find the product of the order and the degree of the differential equation [d/(dx)(xy^2)] · dy/dx+y=0.2022
• Find the general solution of the following differential equation: (d y)/(d x)=e^x-y+x^2 e^-y2022
• Find the general solution of the differential equation: e^dy/dx = x^2.2022
• Find the general solution of the differential equation: log (dy/dx)=ax+by.2022
• Find the general solution of the differential equation: dy/dx=(3 e^2 x+3 e^4 x)/(e^x+e^-x)2022
• Find the general solution of the differential equation sec^2 x · tan y d x+ sec^2 y · tan x d y=0.2022
• Solve the differential equation: log (dy/dx)=x-y.2022
• Find the particular solution of the differential equation (d y)/(d x)=2 y^2, given y=1 when x=1.2022
• Find the general solution of the differential equation x (d y)/(d x)-y+x sin y/x=0.2022
• Find the particular solution of the differential equation x dy/(d x)-y=x^2 · e^x, given y(1)=0. OR Find the general solution of…2022
• Solve the differential equation: dy/dx=(x^2+y^2)/(x y).2022
• Solve the following differential equation: (1+e^y / x) d y+e^y / x(1-y/x) d x=02022
• Find the particular solution of the differential equation (y+3 x^2) (d x)/(d y)=x, given that y=1, when x=1.2022
• Find the particular solution of the differential equation x dy/dx+x cos^2(y/x)=y; given that when x=1, y=(π)/4.2022
• Find the particular solution of the differential equation x (d y)/(d x)+y+1/(1+x^2)=0, given that y(1)=0. OR Find the general…2022
• Solve the following differential equation: (y- sin^2 x) d x+ tan x d y=0 OR Find the general solution of the differential…2022

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