What is the solution for y^{''}+25y=cos(6t) ?

The solution for y^{''}+25y=cos(6t) is y=c_{1}cos(5t)+c_{2}sin(5t)-1/11 cos(6t)

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y^{''}+25y=cos(6t)

y^{^{''}} + 25 y = cos (6 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{11} cos (6 t)

Solution steps

y^{''} (t) + 25 y = cos (6 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{11} cos (6 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{11} cos (6 t)

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

\int \frac{5 x ^{2}}{( x - 1 ) ( x ^{2} + 9 )} d x

x \to 3 lim (x^{2} - 5 x)

\frac{d}{d s} (s^{2} y (s) - 1)

f (x) = x^{2} - 2 x + 1

What is the solution for y^{''}+25y=cos(6t) ?
The solution for y^{''}+25y=cos(6t) is y=c_{1}cos(5t)+c_{2}sin(5t)-1/11 cos(6t)