What is the solution for y^{''}+49y=-49sec^2(7x) ?

The solution for y^{''}+49y=-49sec^2(7x) is y=c_{1}cos(7x)+c_{2}sin(7x)+1-ln(sec(7x)+tan(7x))sin(7x)

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y^{''}+49y=-49sec^2(7x)

y^{^{''}} + 49 y = - 49 sec^{2} (7 x)

y = c_{1} cos (7 x) + c_{2} sin (7 x) + 1 - ln (sec (7 x) + tan (7 x)) sin (7 x)

Solution steps

y^{''} (x) + 49 y = - 49 sec^{2} (7 x)

Solve linear ODE:

y = c_{1} cos (7 x) + c_{2} sin (7 x) + 1 - ln (sec (7 x) + tan (7 x)) sin (7 x)

y = c_{1} cos (7 x) + c_{2} sin (7 x) + 1 - ln (sec (7 x) + tan (7 x)) sin (7 x)

(9 x^{2} + y - 1) - (4 y - x) y^{^{'}} = 0

ln (\frac{1}{1 - x})

\int \frac{1}{x ^{2}} + \frac{4}{x x} + 2 d x

\int x e^{y} d y

\frac{d}{d t} (a e^{t})

What is the solution for y^{''}+49y=-49sec^2(7x) ?
The solution for y^{''}+49y=-49sec^2(7x) is y=c_{1}cos(7x)+c_{2}sin(7x)+1-ln(sec(7x)+tan(7x))sin(7x)