What is the solution for y^{''}-5y^'+4y=3e^xsin(x) ?

The solution for y^{''}-5y^'+4y=3e^xsin(x) is y=c_{1}e^{4x}+c_{2}e^x+9/10 e^xcos(x)-3/10 e^xsin(x)

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y^{''}-5y^'+4y=3e^xsin(x)

y^{^{''}} - 5 y^{^{'}} + 4 y = 3 e^{x} sin (x)

y = c_{1} e^{4 x} + c_{2} e^{x} + \frac{9}{10} e^{x} cos (x) - \frac{3}{10} e^{x} sin (x)

Solution steps

y^{''} (x) - 5 y^{'} (x) + 4 y = 3 e^{x} sin (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{x} + \frac{9}{10} e^{x} cos (x) - \frac{3}{10} e^{x} sin (x)

y = c_{1} e^{4 x} + c_{2} e^{x} + \frac{9}{10} e^{x} cos (x) - \frac{3}{10} e^{x} sin (x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} (12 x^{2} - 6 x)

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

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 9 - e^{x} + e^{4 x}

y^{^{''}} + y = t^{2} + 2

y^{^{''}} - 16 y = 6

What is the solution for y^{''}-5y^'+4y=3e^xsin(x) ?
The solution for y^{''}-5y^'+4y=3e^xsin(x) is y=c_{1}e^{4x}+c_{2}e^x+9/10 e^xcos(x)-3/10 e^xsin(x)