y^{''}-2y^'-15y=3e^{5t}

Lösung

y^{^{''}} - 2 y^{^{'}} - 15 y = 3 e^{5 t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} + \frac{3 e ^{5 t} t}{8}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 15 y = 3 e^{5 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} + \frac{3 e ^{5 t} t}{8}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} + \frac{3 e ^{5 t} t}{8}

y^{^{'''}} + 4 y^{^{''}} - 5 y = x e^{x} + 8

y^{^{''}} - 12 y^{^{'}} + 36 y = e^{6 t} arctan (t)

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 1