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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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