What is the solution for y^{''}+49y=49sec^2(7t) ?

The solution for y^{''}+49y=49sec^2(7t) is y=c_{1}cos(7t)+c_{2}sin(7t)-1+ln(sec(7t)+tan(7t))sin(7t)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} = - 2

4 y + 7 y^{^{'}} + 2 y^{^{''}} = 10 \cdot cos (4 x)

y^{^{''}} - y^{^{'}} + y = sin (t) - 3 e^{2 t}

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{t}

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

What is the solution for y^{''}+49y=49sec^2(7t) ?
The solution for y^{''}+49y=49sec^2(7t) is y=c_{1}cos(7t)+c_{2}sin(7t)-1+ln(sec(7t)+tan(7t))sin(7t)