What is the solution for 10y^{''}+45y^'+2500y=180cos(7pix) ?

The solution for 10y^{''}+45y^'+2500y=180cos(7pix) is

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10y^{''}+45y^'+2500y=180cos(7pix)

10 y^{^{''}} + 45 y^{^{'}} + 2500 y = 180 cos (7 π x)

y = e^{- \frac{9 x}{4}} (c_{1} cos (\frac{3919 x}{4}) + c_{2} sin (\frac{3919 x}{4})) + \frac{2268 π}{9604 π ^{4} - 94031 π ^{2} + 250000} sin (7 π x) + \frac{9 ( 38416 π ^{4} - 392000 π ^{2} + 1000000 )}{- 941192 π ^{6} + 14017038 π ^{4} - 71515500 π ^{2} + 125000000} cos (7 π x)

Solution steps

10 y^{''} (x) + 45 y^{'} (x) + 2500 y = 180 cos (7 π x)

Solve linear ODE:

y = e^{- \frac{9 x}{4}} (c_{1} cos (\frac{3919 x}{4}) + c_{2} sin (\frac{3919 x}{4})) + \frac{2268 π}{9604 π ^{4} - 94031 π ^{2} + 250000} sin (7 π x) + \frac{9 ( 38416 π ^{4} - 392000 π ^{2} + 1000000 )}{- 941192 π ^{6} + 14017038 π ^{4} - 71515500 π ^{2} + 125000000} cos (7 π x)

y = e^{- \frac{9 x}{4}} (c_{1} cos (\frac{3919 x}{4}) + c_{2} sin (\frac{3919 x}{4})) + \frac{2268 π}{9604 π ^{4} - 94031 π ^{2} + 250000} sin (7 π x) + \frac{9 ( 38416 π ^{4} - 392000 π ^{2} + 1000000 )}{- 941192 π ^{6} + 14017038 π ^{4} - 71515500 π ^{2} + 125000000} cos (7 π x)

What is the solution for 10y^{''}+45y^'+2500y=180cos(7pix) ?
The solution for 10y^{''}+45y^'+2500y=180cos(7pix) is