Solve $\frac{d^2y}{dt^2}-\cos t\cdot \frac{dy}{dt}+e^t.y=0$

Solve the differential equation $$\frac{d^2y}{dt^2}-\cos t \cdot \frac{dy}{dt}+e^t.y=0$$

I have attempted with DSolve[{y''[x] - Cos[x]*y'[x] + y[x]*E^x == 0, y[0] == 0, y'[0] == 0}, y[x], x] which gives DSolve[{E^x y[x] - Cos[x] Derivative[1][y][x] + (y^\[Prime]\[Prime])[x] == 0, True, True}, y[x], x]

What is going wrong here and how do I find the solution ?

• y[0],y'[0]are predefined, restart your kernel!. Now Mathematica evaluation shows the input (after a while) and shows that MMA can't solve the ode! Commented Nov 8, 2020 at 21:25
• The solution is the trivial solution y[x] = 0 (by inspection). DSolve won't find it because it can't find the general solution, and it doesn't seem to be able to solve by inspection. Commented Nov 8, 2020 at 22:24
• You can still use NDSolve to get a numerical solution. Commented Nov 9, 2020 at 8:21

This return y[x]=0
Plot[NDSolveValue[{y[0] == 0, y'[0] == 0, y''[t] - Cos[t] y'[t] + E^t y[t] == 0}, y, {t, 0,