What is the solution for y^{''}-2y^'+50y=e^xcos(7x) ?

The solution for y^{''}-2y^'+50y=e^xcos(7x) is y=e^x(c_{1}cos(7x)+c_{2}sin(7x))+(e^xxsin(7x))/(14)

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y^{''}-2y^'+50y=e^xcos(7x)

y^{^{''}} - 2 y^{^{'}} + 50 y = e^{x} cos (7 x)

y = e^{x} (c_{1} cos (7 x) + c_{2} sin (7 x)) + \frac{e ^{x} x sin ( 7 x )}{14}

Solution steps

y^{''} (x) - 2 y^{'} (x) + 50 y = e^{x} cos (7 x)

Solve linear ODE:

y = e^{x} (c_{1} cos (7 x) + c_{2} sin (7 x)) + \frac{e ^{x} x sin ( 7 x )}{14}

y = e^{x} (c_{1} cos (7 x) + c_{2} sin (7 x)) + \frac{e ^{x} x sin ( 7 x )}{14}

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

y^{^{''}} + 25 y^{^{'}} = - 24 t e^{- t}

y^{^{''}} + 4 y^{^{'}} + y = (\frac{e ^{- \frac{x}{2}}}{x ^{2}})

2 y^{^{''}} - 2 y^{^{'}} - 4 y = 2 e^{3 t}

2 x^{^{''}} + 3 x^{^{'}} + 4 x = - 5 cos (t) + sin (t)

What is the solution for y^{''}-2y^'+50y=e^xcos(7x) ?
The solution for y^{''}-2y^'+50y=e^xcos(7x) is y=e^x(c_{1}cos(7x)+c_{2}sin(7x))+(e^xxsin(7x))/(14)