What is the solution for y^{''}-10y^'+29y=87x ?

The solution for y^{''}-10y^'+29y=87x is y=e^{5x}(c_{1}cos(2x)+c_{2}sin(2x))+3x+30/29

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y^{''}-10y^'+29y=87x

y^{^{''}} - 10 y^{^{'}} + 29 y = 87 x

y = e^{5 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 3 x + \frac{30}{29}

Solution steps

y^{''} (x) - 10 y^{'} (x) + 29 y = 87 x

Solve linear ODE:

y = e^{5 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 3 x + \frac{30}{29}

y = e^{5 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 3 x + \frac{30}{29}

(D + 1) 3 y = 5 e - x

y^{^{''}} - 4 y = cos (2 x)

\frac{1}{4} y^{^{''}} + 4 y = 3 tan (4 t) - \frac{1}{2} e^{2 t}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 2 e^{- x}

y^{^{''}} + 4 y = (x^{2} - 3) \cdot sin (2 x)

What is the solution for y^{''}-10y^'+29y=87x ?
The solution for y^{''}-10y^'+29y=87x is y=e^{5x}(c_{1}cos(2x)+c_{2}sin(2x))+3x+30/29