Variables Separable

JEE Main Mathematics · Differential Equations · 18 questions, latest first

• Let y=y(x) be the solution of the differential equation (d y)/(d x)=(1+x+x^2)(1-y+y^2), y(0)=1/2. Then (2 y(1)-1) is equal to20264 April, Shift 1 · Q20
• If the curve y=f(x) passes through the point ( 1, e ) and satisfies the differential equation d y=y(2+ log_e x) d x, x>0, then…20262 April, Shift 1 · Q17
• Let y=y(x) be the solution curve of the differential equation (1+ sin x) (d y)/(d x)+(y+1) cos x=0, y(0)=0. If the curve y=y(x)…20262 April, Shift 1 · Q20
• If y=y(x) satisfies the differential equation 16(√(x+9 √x))(4+√(9+√x)) cos y d y=(1+2 sin y) d x, x>0 and y(256)=(π)/2, y(49)=α,…202622 January, Shift 2 · Q20
• Let a curve y=f(x) pass through the points (0,5) and ( log_e 2, k). If the curve satisfies the differential equation 2(3+y) e^2 x…202523 January, Shift 1 · Q20
• Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x) f^′(y)+f^′(x) f(y) for all x, y ∈ R. Then Σ_n=1^100…202522 January, Shift 1 · Q17
• For a differentiable function f: R → R, suppose f^′(x)=3 f(x)+α, where α ∈ R, f(0)=1 and lim_x →-∞ f(x)=7. Then 9 f(- log_e 3) is…20249 April, Shift 2 · Q26
• The solution curve, of the differential equation 2 y (d y)/(d x)+3=5 (d y)/(d x), passing through the point (0,1) is a conic,…20249 April, Shift 1 · Q11
• Let y=y(x) be the solution of the differential equation (1+y^2) e^tan x d x+ cos^2 x(1+e^2 tan x) d y=0, y(0)=1. Then y((π)/4) is…20248 April, Shift 1 · Q13
• If the solution y(x) of the given differential equation (e^y+1) cos x d x+e^y sin x d y=0 passes through the point ((π)/2, 0),…20246 April, Shift 2 · Q26
• If the solution y=y(x) of the differential equation (x^4+2 x^3+3 x^2+2 x+2) d y-(2 x^2+2 x+3) d x=0 satisfies y(-1)=-(π)/4, then…20244 April, Shift 1 · Q14
• Let α be a non-zero real number. Suppose f: R → R is a differentiable function such that f(0)=2 and lim_x →-∞ f(x)=1. If f^′(x)=α…20241 February, Shift 2 · Q12
• Let y=y(x) be the solution of the differential equation sec x d y+{2(1-x) tan x+x(2-x)} d x=0 such that y(0)=2. Then y(2) is…202430 January, Shift 1 · Q12
• If the solution curve y=y(x) of the differential equation (1+y^2)(1+ log_e x) d x+x d y=0, x>0 passes through the point (1,1) and…202429 January, Shift 1 · Q26
• If y=y(x) is the solution curve of the differential equation (x^2-4) d y-(y^2-3 y) d x=0, x>2, y(4)=3/2 and the slope of the…202427 January, Shift 2 · Q13
• Let x=x(t) and y=y(t) be solutions of the differential equations (d x)/dt+ax=0 and dy/dt+by=0 respectively, a, b ∈ R. Given that…202427 January, Shift 1 · Q13
• The area enclosed by the closed curve C given by the differential equation (d y)/(d x)+(x+a)/(y-2)=0, y(1)=0 is 4 π. Let P and Q…20231 February, Shift 1 · Q71
• Let y=f(x) be the solution of the differential equation y(x+1) d x-x^2 d y=0, y(1)=e. Then lim_x → 0^+ f(x) is equal to202329 January, Shift 1 · Q80