What is the solution for y^{''}-2y^'+y=10cos(x)+8sin(x) ?

The solution for y^{''}-2y^'+y=10cos(x)+8sin(x) is y=c_{1}e^x+c_{2}xe^x-5sin(x)+4cos(x)

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y^{''}-2y^'+y=10cos(x)+8sin(x)

y^{^{''}} - 2 y^{^{'}} + y = 10 cos (x) + 8 sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} - 5 sin (x) + 4 cos (x)

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 10 cos (x) + 8 sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - 5 sin (x) + 4 cos (x)

y = c_{1} e^{x} + c_{2} x e^{x} - 5 sin (x) + 4 cos (x)

What is the solution for y^{''}-2y^'+y=10cos(x)+8sin(x) ?
The solution for y^{''}-2y^'+y=10cos(x)+8sin(x) is y=c_{1}e^x+c_{2}xe^x-5sin(x)+4cos(x)