Solve the following differential equation: `(dy)/(dx)=x\ e^x-5/2+cos^2x`

Explanation

`frac{d y}{d x}=x e^{x}-frac{5}{2}+cos ^{2} x `


`Rightarrow frac{d y}{d x}=x e^{x}-frac{5}{2}+frac{cos 2 x}{2}+frac{1}{2} `


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


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



By Integrating we obtain,


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


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