✓ Board-verified
Mathematics · 2022 · 2 marks
CBSE 2022 · Region 1 · Set 1 · Q1
Find the sum of the order and the degree of the differential equation: (x+dy/dx)^2=(dy/dx)^2+1
Find the sum of the order and the degree of the differential equation : \[\left(x+\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}+1 \]
Marking-scheme solution
Given differential equation can be written as
\[x^{2}+\left(\frac{d y}{d x}\right)^{2}+2 x \frac{d y}{d x}=\left(\frac{d y}{d x}\right)^{2}+1
\]
i.e. \(\displaystyle x^{2}+2 x \frac{d y}{d x}=1 ;\) Order \(\displaystyle =1\), degree \(\displaystyle =1\)
Sum of order and degree \(\displaystyle =1+1=2\)
All Differential Equations questions2022 question paperNCERT solutions: Differential EquationsPractice Differential Equations →
More from Differential Equations
- The integrating factor of the differential equation (1-y^2) (d x)/dy+y x=ay,(-1<y<1) is2023
- The integrating factor for solving the differential equation x dy/dx-y=2 x^2 is:2023
- Product of the order and degree of differential equation 1+(dy/dx)^3=λ((d^3 y)/(dx^3))^2 is:2026
- Solve the differential equation (d y)/(d x)= cos x-2 y.2025
- The solution of the differential equation (d x)/x+(d y)/y=0 is:2023
- 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 equation (1+e^2 x)…2026
- The integrating factor of the differential equation (x+2 y^2) (d y)/(d x)=y(y>0) is:2024
- Find the particular solution of the differential equation dy/dx-y/x+cosec(y/x)=0; given that y=0, when x=1.2025
CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.