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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 1 · Q28
Solve the differential equation (x+2 y^3) d y=y d x.
Solve the differential equation $\displaystyle \left(x+2 y^{3}\right) d y=y d x$.
Marking-scheme solution
Given differential equation can be written as $\displaystyle \dfrac{dx}{dy}-\dfrac{x}{y}=2 y^{2}$
Integrating factor $\displaystyle =e^{\int-\frac{1}{y} d y}=e^{-\log y}=\dfrac{1}{y}$
Solution is $\displaystyle x \cdot \dfrac{1}{y}=\int 2 y\, d y+C$
i.e., $\displaystyle x \cdot \dfrac{1}{y}=y^{2}+C$ or $\displaystyle x=y^{3}+C y$
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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.