y^{''}-3y=e^x

Lösung

y^{^{''}} - 3 y = e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{2} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{2} e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{2} e^{x}

y^{^{''}} + y^{^{'}} + y = sinh (x)

\frac{d ^{2} y}{d t ^{2}} - 4 y = t cos (2 t), y = 0, t = 0

y^{^{''}} + 25 y = 20 sec (5 t)

y^{^{''}} - 1 y = tan (x)

y^{^{'''}} + y^{^{''}} - 4 = 0