y^{''}-4y^'-21y=320e^{-t}

Lösung

y^{^{''}} - 4 y^{^{'}} - 21 y = 320 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 3 t} - 20 e^{- t}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 21 y = 320 e^{- t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 3 t} - 20 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 3 t} - 20 e^{- t}

6 y^{^{''}} - y^{^{'}} - y = 50 e^{\frac{x}{2}} + 4 x^{2} - 5

\frac{d ^{2} y}{d x ^{2}} + 5 y - sin (π x) = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 t

y^{^{''}} - y^{^{'}} = 5 sin (2 t), y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x) sec^{2} (3 x)