Question

Show that y = be^x + ce^2x is a solution of the differential equation \(\frac {d^2y}{dx^2}-3\frac {dy}{dx}+2y=0.\)

Answer 1

We have, y = be^x + ce^2x  .....(i)

Differentiating (i) with respect to x, we get

\(\frac{dy}{dx}=be^x +2ce^{2x}\) ......(ii)

Again differentiating (ii) with respect to x, we get

So, y = be^x + ce^2x satisfies the given differential equation. 

Hence, it is a solution of the given differential equation.