y^{''}-4y=2e^{2x}

Lösung

y^{^{''}} - 4 y = 2 e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{e ^{2 x} x}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{e ^{2 x} x}{2}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{e ^{2 x} x}{2}

y^{^{''}} + y^{^{'}} - 2 y = 1 + t

y^{^{'''}} + 25 y^{^{'}} = tan (5 x)

y^{^{''}} - 2 y^{^{'}} + 5 y = - 8

y^{^{''}} + y^{^{'}} = tan^{2} (x)

\frac{d ^{2} x}{d t ^{2}} + 81 x = 2 sin (9 t)