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

Mathematica Asked by Sooraj S on July 14, 2021

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 ?

One Answer

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

Answered by wuyudi on July 14, 2021

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