Solve the following differential equations: `(x+2)(dy)/(dx)-x^2+4x-9,x!=-2` and `y(0) = 0,`then` y(−4`) is equal to

Explanation

`(x+2) frac{d y}{d x}=x^{2}+4 x-9 `


`Rightarrow int d y=int frac{((x+2)^{2}-13) d x}{(x+2)} `


`Rightarrow y=(frac{x^{2}}{2}+2 x)-13 ln |x+2|+c`


now

`

y(0)=0 Rightarrow 0=-13 ln 2+c Rightarrow c=13` ln `2`



then,


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