What is the solution for y^{''}-8y^'+25y=208sin(3x) ?

The solution for y^{''}-8y^'+25y=208sin(3x) is y=e^{4x}(c_{1}cos(3x)+c_{2}sin(3x))+4sin(3x)+6cos(3x)

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y^{''}-8y^'+25y=208sin(3x)

y^{^{''}} - 8 y^{^{'}} + 25 y = 208 sin (3 x)

y = e^{4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + 4 sin (3 x) + 6 cos (3 x)

Solution steps

y^{''} (x) - 8 y^{'} (x) + 25 y = 208 sin (3 x)

Solve linear ODE:

y = e^{4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + 4 sin (3 x) + 6 cos (3 x)

y = e^{4 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + 4 sin (3 x) + 6 cos (3 x)

y^{^{'}} = \frac{2 x y}{x ^{2} - y ^{2}}

4 x = 4 y - y^{2}, 4 x - y = 0

\int \frac{1}{x ^{2} 7 + x ^{2}} d x

f (x) = e^{7 x} cos (10 x)

\frac{d y}{d x} = x e^{x^{2}}

What is the solution for y^{''}-8y^'+25y=208sin(3x) ?
The solution for y^{''}-8y^'+25y=208sin(3x) is y=e^{4x}(c_{1}cos(3x)+c_{2}sin(3x))+4sin(3x)+6cos(3x)