Solve the following differential equation: `(dy)/(dx)=x^2e^x`

Explanation

`(dy)/(dx)=x^2e^x`


Seperating variables of equation


`Rightarrow d y=x^{2} e^{x} d x`


Integrate both sides of equation,


`Rightarrow int d y=x^{2} int e^{x} d x-int(frac{d}{d x}(x^{2}) int e^{x} d x) d x`


`Rightarrow y=x^{2} e^{x}-2 int x e^{x} d x `


`Rightarrow y=x^{2} e^{x}-2 x int e^{x} d x+2 int(frac{d}{d x}(x) int e^{x} d x) d x`


`Rightarrow y=x^{2} e^{x}-2 x e^{x}+2 e^{x}+C `


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