The general solution of \(\frac{dy}{dx}+\frac yx=x^2\) is
A. \(\frac yx=\frac{x^4}{4}+C\)
B. \(xy=\frac{x^4}{4}+C\)
C. \(xy=\frac{x^3}{3}+C\)
D. \(y=\frac{x^4}{4}+Cx\)
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Answer: B. \(xy=\frac{x^4}{4}+C\)
I.F. \(=e^{\int dx/x}=x\); \(\frac{d}{dx}(xy)=x^3\Rightarrow xy=\frac{x^4}{4}+C\).
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· 23 Oct 2026
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