Show that`\ y=A e^(B x)` is as solution of the differential equation `(d^2y)/(dx^2)=1/y((dy)/(dx))^2dot`

Explanation

Given, `y=A e^(B x)`


Differentiating w.r.t. `x`


`y'=ABe^(Bx)`` \ \ \ \ ...(i) `



Squaring both sides


`(y')^2=(AB)^2e^(2B x)`` \ \ \ \ ...(ii) `



Differentiating again `(i)` w.r.t. `x`


`y''=AB^2e^(Bx)`



Multiplying `(1)/(y)` to `(ii)`


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