What is the solution for y^{''}+9y=3sec(3x) ?

The solution for y^{''}+9y=3sec(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+1/3 ln(cos(3x))cos(3x)+xsin(3x)

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y^{''}+9y=3sec(3x)

y^{^{''}} + 9 y = 3 sec (3 x)

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

Solution steps

y^{''} (x) + 9 y = 3 sec (3 x)

Solve linear ODE:

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

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

5 x e^{2 x}

\frac{d}{d x} (\frac{x ^{2}}{4 - x ^{2} - y ^{2}})

x \to 0 lim (e^{x} + 2 x)

k = 3 \sum \infty \frac{1}{ln ( k )}

\int \frac{1}{x 1 - 4 ln ^{2} ( x )} d x

What is the solution for y^{''}+9y=3sec(3x) ?
The solution for y^{''}+9y=3sec(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+1/3 ln(cos(3x))cos(3x)+xsin(3x)