Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDifferential Equations1 Mark
Question
Write the general solution of the equation $\frac{d y}{d x}+\frac{1}{x} y=$ $x$.
✓
Answer
$P =\frac{1}{x}$ $\therefore$ $ \begin{aligned} \text { I.F. } & =e^{\int P d x}=e^{\int \frac{1}{x} d x} \\ \text { I.F. } & =e^{\log x}=x \\ y . \text { I.F. } & =\int(\text { I.F. } \times \text { Q }) d x \\ y \times x & =\int x \times x d x=\int x^2 d x \end{aligned} $ $ \Rightarrow \quad x y=\frac{x^3}{3}+c $
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