What is the solution for y^{''}+14y^'+100y=10sin(2pi*x)+5sin(pi*x) ?

The solution for y^{''}+14y^'+100y=10sin(2pi*x)+5sin(pi*x) is

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y^{''}+14y^'+100y=10sin(2pix)+5sin(pix)

y^{^{''}} + 14 y^{^{'}} + 100 y = 10 sin (2 π \cdot x) + 5 sin (π \cdot x)

y = e^{- 7 x} (c_{1} cos (51 x) + c_{2} sin (51 x)) + \frac{- 10 π ^{2} + 250}{4 ( - π ^{2} + π ^{4} + 625 )} sin (2 π x) - \frac{- 70 π ^{3} + 1750 π}{- 4 π ^{6} + 104 π ^{4} - 2600 π ^{2} + 62500} cos (2 π x) + \frac{- 5 π ^{2} + 500}{π ^{4} - 4 π ^{2} + 10000} sin (π x) - \frac{- 70 π ^{3} + 7000 π}{- π ^{6} + 104 π ^{4} - 10400 π ^{2} + 1000000} cos (π x)

Solution steps

y^{''} (x) + 14 y^{'} (x) + 100 y = 10 sin (2 π \cdot x) + 5 sin (π \cdot x)

Solve linear ODE:

y = e^{- 7 x} (c_{1} cos (51 x) + c_{2} sin (51 x)) + \frac{- 10 π ^{2} + 250}{4 ( - π ^{2} + π ^{4} + 625 )} sin (2 π x) - \frac{- 70 π ^{3} + 1750 π}{- 4 π ^{6} + 104 π ^{4} - 2600 π ^{2} + 62500} cos (2 π x) + \frac{- 5 π ^{2} + 500}{π ^{4} - 4 π ^{2} + 10000} sin (π x) - \frac{- 70 π ^{3} + 7000 π}{- π ^{6} + 104 π ^{4} - 10400 π ^{2} + 1000000} cos (π x)

y = e^{- 7 x} (c_{1} cos (51 x) + c_{2} sin (51 x)) + \frac{- 10 π ^{2} + 250}{4 ( - π ^{2} + π ^{4} + 625 )} sin (2 π x) - \frac{- 70 π ^{3} + 1750 π}{- 4 π ^{6} + 104 π ^{4} - 2600 π ^{2} + 62500} cos (2 π x) + \frac{- 5 π ^{2} + 500}{π ^{4} - 4 π ^{2} + 10000} sin (π x) - \frac{- 70 π ^{3} + 7000 π}{- π ^{6} + 104 π ^{4} - 10400 π ^{2} + 1000000} cos (π x)

\int \frac{1}{( x ^{2} + 1 ) ^{2} ( x ^{2} - 1 )} d x

3 y^{^{''}} + y^{^{'}} + 2 y = 0

\int \frac{4 x ^{2}}{x ^{3} + 8} d x

\frac{\partial}{\partial x} ((1 - x - 4 y)^{\frac{1}{2}})

\frac{\partial}{\partial x} (5 e^{x^{5} y})

What is the solution for y^{''}+14y^'+100y=10sin(2pi*x)+5sin(pi*x) ?
The solution for y^{''}+14y^'+100y=10sin(2pi*x)+5sin(pi*x) is