What is the solution for y^{''}-2y^'+5y=17cos(2x) ?

The solution for y^{''}-2y^'+5y=17cos(2x) is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))-4sin(2x)+cos(2x)

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y^{''}-2y^'+5y=17cos(2x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 17 cos (2 x)

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

Solution steps

y^{''} (x) - 2 y^{'} (x) + 5 y = 17 cos (2 x)

Solve linear ODE:

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

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

\int x (12 x + 8) d x

x \to 0 lim (e^{- \frac{1}{x}})

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

\int (- 9 x^{2} + 9 x + 2) d x

y = (x^{3} + 8 x^{2})^{- 1}

What is the solution for y^{''}-2y^'+5y=17cos(2x) ?
The solution for y^{''}-2y^'+5y=17cos(2x) is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))-4sin(2x)+cos(2x)