What is the solution for y^{''}+25y=40sin(5x) ?

The solution for y^{''}+25y=40sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-4xcos(5x)

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y^{''}+25y=40sin(5x)

y^{^{''}} + 25 y = 40 sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 4 x cos (5 x)

Solution steps

y^{''} (x) + 25 y = 40 sin (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 4 x cos (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 4 x cos (5 x)

What is the solution for y^{''}+25y=40sin(5x) ?
The solution for y^{''}+25y=40sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-4xcos(5x)