y^{''}-2y^'-15y=(6t+3tt+1)e^t

Lösung

y^{^{''}} - 2 y^{^{'}} - 15 y = (6 t + 3 tt + 1) e^{t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{3 e ^{t} t ^{2}}{16} - \frac{3 e ^{t} t}{8} - \frac{11}{128} e^{t}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 15 y = (6 t + 3 tt + 1) e^{t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{3 e ^{t} t ^{2}}{16} - \frac{3 e ^{t} t}{8} - \frac{11}{128} e^{t}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{3 e ^{t} t ^{2}}{16} - \frac{3 e ^{t} t}{8} - \frac{11}{128} e^{t}

25 y + 12 y^{^{'}} + 4 y^{^{''}} = - 2

y^{^{'''}} - y^{^{'}} = 4 x^{2} + 5 x - 2

y^{^{''}} + 3 y^{^{'}} + 2 y = 1 + 4 x e^{- 3 x}

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = e^{t}

y^{^{''}} - 2 y^{^{'}} + 5 y = 1 + x, y (0) = 0, y^{^{'}} (0) = 4