2y^{''}+3y^'-2y=0,y(0)=1,y(0)=7

Lösung

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 0, y (0) = 1, y (0) = 7

y = (1 - c_{2}) e^{\frac{t}{2}} + c_{2} e^{- 2 t}

Schritte zur Lösung

2 y^{''} (t) + 3 y^{'} (t) - 2 y = 0

Solve linear ODE:

y = (1 - c_{2}) e^{\frac{t}{2}} + c_{2} e^{- 2 t}

y = (1 - c_{2}) e^{\frac{t}{2}} + c_{2} e^{- 2 t}

2 y^{^{''}} + 9 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

\frac{d ^{2} x}{d t ^{2}} + 2 a \frac{d x}{d t} + b^{2} x = 0, a < b

x^{^{''}} + 4 x^{^{'}} + 5 x = 0, x (0) = 0, x^{^{'}} (0) = 4

y^{^{''}} + 81 y = 0, y (0) = 3, y^{^{'}} (0) = 8

14 y^{^{''}} - 15 y^{^{'}} + y = 0, y (0) = 14, y^{^{'}} (0) = \frac{1}{14}