What is the solution for y^{''}+100y=200sin(10x),y^'(0)=0,y^{''}(0)=0 ?

The solution for y^{''}+100y=200sin(10x),y^'(0)=0,y^{''}(0)=0 is y=-10xcos(10x)+sin(10x)

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y^{''}+100y=200sin(10x),y^'(0)=0,y^{''}(0)=0

y^{^{''}} + 100 y = 200 sin (10 x), y^{^{'}} (0) = 0, y^{^{''}} (0) = 0

y = - 10 x cos (10 x) + sin (10 x)

Solution steps

y^{''} (x) + 100 y = 200 sin (10 x)

Solve linear ODE:

y = - 10 x cos (10 x) + sin (10 x)

y = - 10 x cos (10 x) + sin (10 x)

y^{^{''}} + 9 y = cos (3 x) + sin (3 x), y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 6} e^{3 t}

y^{^{''}} + 5 y^{^{'}} + 6 y = 12 e^{t}, y (0) = - 11, y (0) = 31

y^{^{''}} + y^{^{'}} - y = t^{3}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{x s e c (x)}

What is the solution for y^{''}+100y=200sin(10x),y^'(0)=0,y^{''}(0)=0 ?
The solution for y^{''}+100y=200sin(10x),y^'(0)=0,y^{''}(0)=0 is y=-10xcos(10x)+sin(10x)