Aspire Faculty ID #18326 · Topic: AMU MCA 2017 · Just now
AMU MCA 2017

The general solution of differential equation $\frac{dy}{dx}+2xy=2e^{-x^2}$ is

Solution

$ \frac{dy}{dx}+2xy=2e^{-x^2} $ Here, $P=2x$ $ \text{I.F.}=e^{\int 2x dx}=e^{x^2} $ Multiply both sides: $ y e^{x^2}=\int 2e^{-x^2} \cdot e^{x^2} dx + C $ $ =\int 2dx + C =2x + C $ $ \Rightarrow y=(2x+C)e^{-x^2} $
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