x^{''}+4x=4sec^2(2t)

Lösung

x^{^{''}} + 4 x = 4 sec^{2} (2 t)

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

Schritte zur Lösung

x^{''} (t) + 4 x = 4 sec^{2} (2 t)

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 8 y = 2 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{x} cos (2 x)

y^{^{''}} + y = cos (- t + \frac{π}{2}), y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} + y = t^{2} sin (t), y (0) = 0, y^{^{'}} (0) = 0