What is the solution for y^{''}+9y=3sec(3t) ?

The solution for y^{''}+9y=3sec(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+1/3 ln(cos(3t))cos(3t)+tsin(3t)

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y^{''}+9y=3sec(3t)

y^{^{''}} + 9 y = 3 sec (3 t)

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

Solution steps

y^{''} (t) + 9 y = 3 sec (3 t)

Solve linear ODE:

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

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

f (x) = cos (x^{2}) \cdot 2 x

y = x + 1, y = 9 - x^{2}, x = - 1, x = 2

\int (sin^{4} (x) cos^{2} (x)) d x

\int \frac{4 x ^{2} + 3 x + 4}{( x ^{2} + 1 ) ^{2}} d x

\int_{- 1}^{0} \frac{30 e ^{\frac{1}{x}}}{x ^{3}} d x

What is the solution for y^{''}+9y=3sec(3t) ?
The solution for y^{''}+9y=3sec(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+1/3 ln(cos(3t))cos(3t)+tsin(3t)