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

Lösung

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

y = (3 - \frac{1}{5}) e^{t} + \frac{1}{5} e^{- 4 t}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) - 4 y = 0

Solve linear ODE:

y = (3 - \frac{1}{5}) e^{t} + \frac{1}{5} e^{- 4 t}

y = (3 - \frac{1}{5}) e^{t} + \frac{1}{5} e^{- 4 t}

y^{^{''}} + 10 y^{^{'}} + 21 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} + 9.25 y = 0, y^{^{'}} (0) = 8

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 5 x = 0, x (0) = 1

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

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 145 y = 0