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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 e^{3 x}

y^{^{''}} - y^{^{'}} = e^{x} cos (x)

y^{^{''}} + 2 y^{^{'}} + y = e^{- 2 t}

y^{^{''}} + y = - sec^{2} (x)

y^{^{''}} + y = x^{2} + 2

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