What is the solution for y^{''}-5y^'+4y=-sin(5t) ?

The solution for y^{''}-5y^'+4y=-sin(5t) is y=c_{1}e^{4t}+c_{2}e^t+21/1066 sin(5t)-25/1066 cos(5t)

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y^{''}-5y^'+4y=-sin(5t)

y^{^{''}} - 5 y^{^{'}} + 4 y = - sin (5 t)

y = c_{1} e^{4 t} + c_{2} e^{t} + \frac{21}{1066} sin (5 t) - \frac{25}{1066} cos (5 t)

Solution steps

y^{''} (t) - 5 y^{'} (t) + 4 y = - sin (5 t)

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{t} + \frac{21}{1066} sin (5 t) - \frac{25}{1066} cos (5 t)

y = c_{1} e^{4 t} + c_{2} e^{t} + \frac{21}{1066} sin (5 t) - \frac{25}{1066} cos (5 t)

y^{^{'}} = \frac{x}{( 1 + 2 y )}

x, x - 2, [0, 4]

\frac{d ^{3}}{d x ^{3}} (3 t^{3} - \frac{2}{t ^{2}})

\int (x^{3} + x + \frac{1}{x ^{3}}) d x

\int_{0}^{\frac{π}{2}} - 10 sin^{2} (3 x) d x

What is the solution for y^{''}-5y^'+4y=-sin(5t) ?
The solution for y^{''}-5y^'+4y=-sin(5t) is y=c_{1}e^{4t}+c_{2}e^t+21/1066 sin(5t)-25/1066 cos(5t)