CBSE 2022 · Region 2 · Set 1 · Q9 · 3 marks
Find the particular solution of the differential equation $\displaystyle \left(\mathrm{y}+3 \mathrm{x}^{2}\right) \frac{d \mathrm{x}}{d \mathrm{y}}=\mathrm{x}$, given that $\displaystyle \mathrm{y}=1$, when $\displaystyle \mathrm{x}=1$.
Marking-scheme solution
Given differential equation can be written as
\[x \frac{d y}{d x}-y=3 x^{2} \text { or } \frac{d y}{d x}-\frac{1}{x} y=3 x
\]
I.F \(\displaystyle =e^{\int-\frac{1}{x} d x}=e^{-\log x}=-x^{-1}=\frac{1}{x}\)
Solution is \(\displaystyle y \cdot \frac{1}{x}=\int 3 x \frac{1}{x} d x+C\)
\[\frac{y}{x}=3 x+C
\]
Differential EquationsGeneral and Particular Solutions of a Differential EquationApplyshort_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.