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given:
![\frac{dy}{dx}= ae^{2x}\left ( 2 \right )+0\left [ By\: chain\: rule \right ]](https://entrancecorner.codecogs.com/gif.latex?%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20ae%5E%7B2x%7D%5Cleft%20%28%202%20%5Cright%20%29+0%5Cleft%20%5B%20By%5C%3A%20chain%5C%3A%20rule%20%5Cright%20%5D)
![\Rightarrow \frac{d^{2}y}{dx^{2}}= \frac{2dy}{dx}-\left [ using\left ( i \right ) \right ]](https://entrancecorner.codecogs.com/gif.latex?%5CRightarrow%20%5Cfrac%7Bd%5E%7B2%7Dy%7D%7Bdx%5E%7B2%7D%7D%3D%20%5Cfrac%7B2dy%7D%7Bdx%7D-%5Cleft%20%5B%20using%5Cleft%20%28%20i%20%5Cright%20%29%20%5Cright%20%5D)
this is the required differential equation
On differentiating w.r.t x, we get
Again differentiating w.r.t x,