What is the solution for y^{''}+y=10sin(2t)+7tcos(2t) ?

The solution for y^{''}+y=10sin(2t)+7tcos(2t) is y=c_{1}cos(t)+c_{2}sin(t)-(7tcos(2t))/3-2/9 sin(2t)

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y^{''}+y=10sin(2t)+7tcos(2t)

y^{^{''}} + y = 10 sin (2 t) + 7 t cos (2 t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{7 t cos ( 2 t )}{3} - \frac{2}{9} sin (2 t)

Solution steps

y^{''} (t) + y = 10 sin (2 t) + 7 t cos (2 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) - \frac{7 t cos ( 2 t )}{3} - \frac{2}{9} sin (2 t)

y = c_{1} cos (t) + c_{2} sin (t) - \frac{7 t cos ( 2 t )}{3} - \frac{2}{9} sin (2 t)

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 e^{5 x}

y^{^{''}} + 8 y^{^{'}} + 16 y = - 5 x e^{- 3 x} + 3 e^{- 4 x} - 4

y^{^{''}} - 16 y^{^{'}} + 64 y = (x + 1) e^{x}

y^{^{''}} - 4 y^{^{'}} + 8 y = x^{3} + x

y^{^{''}} + 4 y = 6 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 3

What is the solution for y^{''}+y=10sin(2t)+7tcos(2t) ?
The solution for y^{''}+y=10sin(2t)+7tcos(2t) is y=c_{1}cos(t)+c_{2}sin(t)-(7tcos(2t))/3-2/9 sin(2t)