What is the solution for 0.1x^{''}+10x=100sin(ct) ?

The solution for 0.1x^{''}+10x=100sin(ct) is x=c_{1}cos(10t)+c_{2}sin(10t)+(1000sin(ct))/(-c^2+100)

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0.1x^{''}+10x=100sin(ct)

0.1 x^{^{''}} + 10 x = 100 sin (c t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{1000 sin ( c t )}{- c ^{2} + 100}

Solution steps

0.1 x^{''} (t) + 10 x = 100 sin (c t)

Solve linear ODE:

x = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{1000 sin ( c t )}{- c ^{2} + 100}

x = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{1000 sin ( c t )}{- c ^{2} + 100}

What is the solution for 0.1x^{''}+10x=100sin(ct) ?
The solution for 0.1x^{''}+10x=100sin(ct) is x=c_{1}cos(10t)+c_{2}sin(10t)+(1000sin(ct))/(-c^2+100)