What is the solution for y^{''}+25y=5sec(5t) ?

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

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y^{''}+25y=5sec(5t)

y^{^{''}} + 25 y = 5 sec (5 t)

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

Solution steps

y^{''} (t) + 25 y = 5 sec (5 t)

Solve linear ODE:

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

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

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