What is the solution for y^{''}-4y^'+3y=4cos(x)-3sin(x) ?

The solution for y^{''}-4y^'+3y=4cos(x)-3sin(x) is y=c_{1}e^{3x}+c_{2}e^x-11/10 sin(x)-1/5 cos(x)

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

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

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{11}{10} sin (x) - \frac{1}{5} cos (x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{11}{10} sin (x) - \frac{1}{5} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{11}{10} sin (x) - \frac{1}{5} cos (x)

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 3

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 t e^{3 t}

y^{^{''}} - 9 y^{^{'}} + 14 y = 30 t - 34

y^{^{''}} + y = 6 sin (2 t), y (0) = 3, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + 4 y = x

What is the solution for y^{''}-4y^'+3y=4cos(x)-3sin(x) ?
The solution for y^{''}-4y^'+3y=4cos(x)-3sin(x) is y=c_{1}e^{3x}+c_{2}e^x-11/10 sin(x)-1/5 cos(x)