CBSE 2022 · Region 1 · Set 3 · Q9 · 3 marks
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
\[\frac{v^{2}}{2}=\log |x|+C
\]
\[\frac{y^{2}}{2 x^{2}}=\log |x|+C
\]
Differential EquationsMethods of Solving First Order, First Degree Differential EquationsApplyshort_answermedium
More from Differential Equations
- The integrating factor of the differential equation (1-y^2) (d x)/(dy)+y x=ay,(-1<y<1) is2023 · asked 3×
- The integrating factor of the differential equation (x+2 y^2) (d y)/(d x)=y(y 0) is:2024 · asked 3×
- The integrating factor of differential equation R (d x)/(dy)+P x=Q where P, Q, R are functions of y is2026 · asked 3×
- Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if…2025 · asked 3×
- A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time.…2024 · asked 3×
- Degree of the differential equation sin x+ cos ((d y)/(d x))=y^2 is2023 · asked 3×
- If p and q are respectively the order and degree of the differential equation /(d x)((dy)/(d x))^3=0, then…2025 · asked 3×
- Find the particular solution of the differential equation (dy)/(dx)=(x+y)/(x), y(1)=0. OR Find the general…2023 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.