y^{''}+4y=4sec^2(2x)

Lösung

y^{^{''}} + 4 y = 4 sec^{2} (2 x)

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

Schritte zur Lösung

y^{''} (x) + 4 y = 4 sec^{2} (2 x)

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = x

y^{^{''}} + 4 y + 4 y = (3 + x) e^{- 2 x}

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 e^{- 2 x} + 2 x

x^{^{''}} + 4 x^{^{'}} + 3 x = 1

(D - 1)^{2} y = (e^{2 x} + sin (2 x))