625x^{''}+100x^'+3x=0,x(0)=25,x^'(0)=-2

Lösung

625 x^{^{''}} + 100 x^{^{'}} + 3 x = 0, x (0) = 25, x^{^{'}} (0) = - 2

x = (25 - \frac{25}{2}) e^{- \frac{t}{25}} + \frac{25}{2} e^{- \frac{3 t}{25}}

Schritte zur Lösung

625 x^{''} (t) + 100 x^{'} (t) + 3 x = 0

Solve linear ODE:

x = (25 - \frac{25}{2}) e^{- \frac{t}{25}} + \frac{25}{2} e^{- \frac{3 t}{25}}

x = (25 - \frac{25}{2}) e^{- \frac{t}{25}} + \frac{25}{2} e^{- \frac{3 t}{25}}

2 \cdot \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

16 y^{^{''}} - y = 0, y (- 4) = 1, y^{^{'}} (- 4) = - 1

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 6 - 6 e^{4}, y (1) = 0

y^{^{''}} - \frac{3}{2} y^{^{'}} - y = 0