✓ Board-verified
Mathematics · 2022 · 3 marks
Differential EquationsMethods of Solving First Order, First Degree Differential Equations3 marksApplyshort answer
CBSE 2022 · Region 1 · Set 3 · Q9
Solve the differential equation: dy/dx=(x^2+ y^2)/(x y).
Solve the differential equation : $\displaystyle \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{x^{2}+\mathrm{y}^{2}}{x \mathrm{y}}$.
Marking-scheme solution
Let \(\displaystyle y=v x \quad \frac{d y}{d x}=v+x \frac{d v}{d x}\)
\[v+x \frac{d v}{d x}=\frac{1+v^{2}}{v}
\]
Gives \(\displaystyle x \frac{d v}{d x}=\frac{1}{v}\)
\[v d v=\frac{d x}{x}
\]
Integrating we get
\[\frac{v^{2}}{2}=\log |x|+C
\]
\[\frac{y^{2}}{2 x^{2}}=\log |x|+C
\]
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.