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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 ?

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    $\begingroup$ 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! $\endgroup$
    – Ulrich Neumann
    Commented Nov 8, 2020 at 21:25
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    $\begingroup$ 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. $\endgroup$
    – Michael E2
    Commented Nov 8, 2020 at 22:24
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    $\begingroup$ You can still use NDSolve to get a numerical solution. $\endgroup$
    – Daniel Huber
    Commented Nov 9, 2020 at 8:21

1 Answer 1

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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, 
10}][x], {x, 0, 10}]

enter image description here

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