What is the solution for (d^2y)/(dx^2)+y=tan(x) ?

The solution for (d^2y)/(dx^2)+y=tan(x) is y=c_{1}cos(x)+c_{2}sin(x)-cos(x)ln(tan(x)+sec(x))

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(d^2y)/(dx^2)+y=tan(x)

\frac{d ^{2} y}{d x ^{2}} + y = tan (x)

y = c_{1} cos (x) + c_{2} sin (x) - cos (x) ln (tan (x) + sec (x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = tan (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - cos (x) ln (tan (x) + sec (x))

y = c_{1} cos (x) + c_{2} sin (x) - cos (x) ln (tan (x) + sec (x))

y^{^{''}} + 10 y^{^{'}} + 25 y = 100 sin (5 x)

(d^{2} + 1) y = sin (x)

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2 x} (cos (x) - 5 sin (x))

y^{^{''}} + 5 y^{^{'}} + 4 y = e^{- t}

y^{^{''}} + 49 y = 11 sec^{2} (7 t)

What is the solution for (d^2y)/(dx^2)+y=tan(x) ?
The solution for (d^2y)/(dx^2)+y=tan(x) is y=c_{1}cos(x)+c_{2}sin(x)-cos(x)ln(tan(x)+sec(x))