The differential equation `x(dy)/(dx)-y=x^2,` has the general solution a. `y-x^3=2c x` b. `2y-x^3=c x` c. `2y+x^2=2c x` d. `y+x^2=2c x`

Explanation

`x frac{d y}{d x}-y=x^{2}`

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Rightarrow frac{d y}{d x}-frac{y}{x}=frac{x^{2}}{y^{2}}`

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frac{d y}{d x}-(frac{1}{x}) y=x`

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because frac{{dy}}{{dx}}+{py}={Q}`

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{p}=frac{-1}{{x}}, {Q}={x}`

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If e^{int p d x}=e^{int-frac{1}{x} d x}=e^{-log x}`

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=e^{log x-1}=frac{1}{x}`

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