y^{''}-8y^'+15y=64e^t

Lösung

y^{^{''}} - 8 y^{^{'}} + 15 y = 64 e^{t}

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

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 15 y = 64 e^{t}

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 3 cos (x)

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 3 e^{7 x}

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} - 6 y = t + e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = 68 cos (3 x)

x^{^{''}} - 9 x - 1 = 0