What is the solution for x^{''}+49x=96cos(5t) ?

The solution for x^{''}+49x=96cos(5t) is x=c_{1}cos(7t)+c_{2}sin(7t)+4cos(5t)

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x^{''}+49x=96cos(5t)

x^{^{''}} + 49 x = 96 cos (5 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 4 cos (5 t)

Solution steps

x^{''} (t) + 49 x = 96 cos (5 t)

Solve linear ODE:

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 4 cos (5 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 4 cos (5 t)

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

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{2 x} + 1

y^{^{''}} - y^{^{'}} - 2 y = 5 e^{4 x} + 6 x

What is the solution for x^{''}+49x=96cos(5t) ?
The solution for x^{''}+49x=96cos(5t) is x=c_{1}cos(7t)+c_{2}sin(7t)+4cos(5t)