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Mathematics · 2022 · 2 marks
Differential EquationsGeneral and Particular Solutions of a Differential Equation2 marksApplyvery short answer
CBSE 2022 · Region 2 · Set 2 · Q6
Find the particular solution of the differential equation (d y)/(d x)=2 y^2, given y =1 when x =1.
Find the particular solution of the differential equation $\displaystyle \frac{d \mathrm{y}}{d \mathrm{x}}=2 \mathrm{y}^{2}$, given $\displaystyle \mathrm{y}=1$ when $\displaystyle \mathrm{x}=1$.
Marking-scheme solution
Given differential equation can be written as
\[\begin{aligned}
& \frac{d y}{y^{2}}=2 d x \\
& \int \frac{d y}{y^{2}}=2 \int d x \\
& \frac{-1}{y}=2 x+C
\end{aligned}
\]
putting \(\displaystyle x=1, y=1\) gives \(\displaystyle C=-3\)
\[\therefore-\frac{1}{y}=2 x-3
\]
Or \(\displaystyle y=\frac{-1}{2 x-3}\)
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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.