What is the solution for y^{''}+25y=-25sec^2(5x) ?

The solution for y^{''}+25y=-25sec^2(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+1-ln(sec(5x)+tan(5x))sin(5x)

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y^{''}+25y=-25sec^2(5x)

y^{^{''}} + 25 y = - 25 sec^{2} (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + 1 - ln (sec (5 x) + tan (5 x)) sin (5 x)

Solution steps

y^{''} (x) + 25 y = - 25 sec^{2} (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + 1 - ln (sec (5 x) + tan (5 x)) sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + 1 - ln (sec (5 x) + tan (5 x)) sin (5 x)

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\int x cos (6 x) d x

What is the solution for y^{''}+25y=-25sec^2(5x) ?
The solution for y^{''}+25y=-25sec^2(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+1-ln(sec(5x)+tan(5x))sin(5x)