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Mathematics · 2022 · 3 marks
Differential EquationsGeneral and Particular Solutions of a Differential Equation3 marksApplyshort answer
CBSE 2022 · Region 2 · Set 1 · Q9
Find the particular solution of the differential equation ( y +3 x^2) (d x)/(d y)= x, given that y =1, when x =1.
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 \(\displaystyle y \cdot \frac{1}{x}=\int 3 x \frac{1}{x} d x+C\)
\[\frac{y}{x}=3 x+C
\]
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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.