What is the solution for y^{''}+16y=6tan(4x) ?

The solution for y^{''}+16y=6tan(4x) is y=c_{1}cos(4x)+c_{2}sin(4x)-(3cos(4x)ln(tan(4x)+sec(4x)))/8

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y^{''}+16y=6tan(4x)

y^{^{''}} + 16 y = 6 tan (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{3 cos ( 4 x ) ln ( tan ( 4 x ) + sec ( 4 x ) )}{8}

Solution steps

y^{''} (x) + 16 y = 6 tan (4 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{3 cos ( 4 x ) ln ( tan ( 4 x ) + sec ( 4 x ) )}{8}

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{3 cos ( 4 x ) ln ( tan ( 4 x ) + sec ( 4 x ) )}{8}

\frac{d y}{d x}, x e^{y} - 10 x + 3 y = 0

(sin (3 x))^{l n (x)}

\frac{\partial}{\partial x} (2 x + y^{2})

\frac{d}{d x} (arcsinh (tan (x)))

\frac{d}{d x} (8 + 3 x^{2})

What is the solution for y^{''}+16y=6tan(4x) ?
The solution for y^{''}+16y=6tan(4x) is y=c_{1}cos(4x)+c_{2}sin(4x)-(3cos(4x)ln(tan(4x)+sec(4x)))/8