CBSE 2025 · Region 5 · Set 1 · Q28 · 3 marks
Find the particular solution of the differential equation \[\left[\mathrm{x} \sin ^{2}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)-\mathrm{y}\right] d \mathrm{x}+\mathrm{x} d \mathrm{y}=0 \] given that $\displaystyle \mathrm{y}=\frac{\pi}{4}$, when $\displaystyle \mathrm{x}=1$.
Marking-scheme solution
\[\begin{aligned}
& {\left[\mathrm{x} \cdot \sin ^{2} \frac{\mathrm{y}}{\mathrm{x}}-\mathrm{y}\right] \cdot d \mathrm{x}+\mathrm{x} \cdot d \mathrm{y}=0} \\
& \Rightarrow \frac{d \mathrm{y}}{d \mathrm{x}}=\frac{\mathrm{y}}{\mathrm{x}}-\sin ^{2} \frac{\mathrm{y}}{\mathrm{x}}
\end{aligned}
\]
$\displaystyle \Rightarrow \cot \frac{\mathrm{y}}{\mathrm{x}}=\log |\mathrm{x}|+1$
Differential EquationsMethods of Solving First Order, First Degree Differential EquationsApplyshort_answerhard
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.