(d^2y)/(dt^2)+4y=4sec^2(2t)

Lösung

\frac{d ^{2} y}{d t ^{2}} + 4 y = 4 sec^{2} (2 t)

y = 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

\frac{d ^{2} y}{d t ^{2}} + 4 y = 4 sec^{2} (2 t)

Solve linear ODE:

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

y^{^{''}} + 5 y^{^{'}} + 6 y = - 19 t e^{2 t}

y^{^{''}} + \frac{1}{2} y^{^{'}} + y = cos (t)

y^{^{'''}} - 4 y^{^{'}} = 3 x - 1

y^{^{''}} - y^{^{'}} + 361 y = 19 sin (19 t)