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Mathematics · 2026 · 3 marks
Differential EquationsMethods of Solving First Order, First Degree Differential Equations3 marksApplyshort answer
CBSE 2026 · Region 5 · Set 3 · Q28
Solve the differential equation ( x - sin y ) d y + tan y d x =0.
Solve the differential equation $\displaystyle (\mathrm{x}-\sin \mathrm{y}) d \mathrm{y}+\tan \mathrm{y}\, d \mathrm{x}=0$.
Marking-scheme solution
Given differential equation can be written as $\displaystyle \dfrac{dx}{dy}+\dfrac{x}{\tan y}=\cos y$
Integrating factor $\displaystyle =e^{\int \frac{1}{\tan y} d y}=e^{\log \sin y}=\sin y$
Solution is $\displaystyle x \cdot \sin y=\int \cos y \sin y\, d y+C$
i.e., $\displaystyle x \cdot \sin y=\dfrac{\sin^{2} y}{2}+C$ or $\displaystyle x=\dfrac{\sin y}{2}+\dfrac{C}{\sin y}$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.