Solve the following differential equation: `(dy)/(dx)+2x=e^(3x)`

Explanation

`frac{d y}{d x}+2 x=e^{3 x} `


`Rightarrow frac{d y}{d x}=e^{3 x}-2 x `


`Rightarrow d y=(e^{3 x}-2 x) d x `


`text { Integrating both sides, we get } `


`Rightarrow int d y=int(e^{3 x}-2 x) d x `


`Rightarrow y=frac{e^{3 x}}{3}-2 frac{x^{2}}{2}+C `


`Rightarrow y=frac{e^{3 x}}{3}-x^{2}+C `


`Rightarrow y+x^{2}=frac{e^{3 x}}{3}+C `


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