What is the solution for y^{''}+25y=cos(3t) ?

The solution for y^{''}+25y=cos(3t) is y=c_{1}cos(5t)+c_{2}sin(5t)+1/16 cos(3t)

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y^{''}+25y=cos(3t)

y^{^{''}} + 25 y = cos (3 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{16} cos (3 t)

Solution steps

y^{''} (t) + 25 y = cos (3 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{16} cos (3 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{16} cos (3 t)

\int_{0}^{\infty} E (t) d t

\frac{d}{d x} (2 x^{3})

\int (e^{x^{3}}) d x

\frac{d}{d x} (\frac{10}{3 x ^{3}})

\frac{\partial}{\partial x} (y \cdot arcsin (\frac{x}{y}))

What is the solution for y^{''}+25y=cos(3t) ?
The solution for y^{''}+25y=cos(3t) is y=c_{1}cos(5t)+c_{2}sin(5t)+1/16 cos(3t)