Show that the equation of the curve whose slope at any point is equal to `y+2x` and which passes through the origin is `y+2(x+1)=2e^(2x)dot`

Explanation

According to the question,

`frac{d y}{d x}=y+2 x `

`Rightarrow frac{d y}{d x}-y=2 x ldots .(1)`

Clearly, it is a linear differential equation of the form


`frac{d y}{d x}+P y=Q `

`text { where } P=-1 text { and } Q=2 {x} `

`therefore I . F .=e^{int P d x} `

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