What is the solution for y^{''}+a^2y=sin(b*t) ?

The solution for y^{''}+a^2y=sin(b*t) is y=c_{1}cos(at)+c_{2}sin(at)+(sin(bt))/(a^2-b^2)

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y^{''}+a^2y=sin(b*t)

y^{^{''}} + a^{2} y = sin (b \cdot t)

y = c_{1} cos (a t) + c_{2} sin (a t) + \frac{sin ( b t )}{a ^{2} - b ^{2}}

Solution steps

y^{''} (t) + a^{2} y = sin (b \cdot t)

Solve linear ODE:

y = c_{1} cos (a t) + c_{2} sin (a t) + \frac{sin ( b t )}{a ^{2} - b ^{2}}

y = c_{1} cos (a t) + c_{2} sin (a t) + \frac{sin ( b t )}{a ^{2} - b ^{2}}

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What is the solution for y^{''}+a^2y=sin(b*t) ?
The solution for y^{''}+a^2y=sin(b*t) is y=c_{1}cos(at)+c_{2}sin(at)+(sin(bt))/(a^2-b^2)