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

The solution for y^{''}-5y^'+4y=5sin(5t) is y=c_{1}e^{4t}+c_{2}e^t-105/1066 sin(5t)+125/1066 cos(5t)

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

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

y = c_{1} e^{4 t} + c_{2} e^{t} - \frac{105}{1066} sin (5 t) + \frac{125}{1066} cos (5 t)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{t} - \frac{105}{1066} sin (5 t) + \frac{125}{1066} cos (5 t)

y = c_{1} e^{4 t} + c_{2} e^{t} - \frac{105}{1066} sin (5 t) + \frac{125}{1066} cos (5 t)

\int_{1}^{e^{x}} ln (t) d t

\int F (x) d x

\frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}} + ln (x y z))

\int tan^{7} (x) sec^{4} (x) d x

x \to - 2 lim (5 (3 x^{2} - 24 x + 3))

What is the solution for y^{''}-5y^'+4y=5sin(5t) ?
The solution for y^{''}-5y^'+4y=5sin(5t) is y=c_{1}e^{4t}+c_{2}e^t-105/1066 sin(5t)+125/1066 cos(5t)