y^{''}+5y^'-24y=0,y(0)=a,y^'(0)=80

Lösung

y^{^{''}} + 5 y^{^{'}} - 24 y = 0, y (0) = a, y^{^{'}} (0) = 80

y = e^{3 t} (a + \frac{80 - 3 a}{11}) - \frac{e ^{- 8 t} ( 80 - 3 a )}{11}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) - 24 y = 0

Solve linear ODE:

y = e^{3 t} (a + \frac{80 - 3 a}{11}) - \frac{e ^{- 8 t} ( 80 - 3 a )}{11}

y = e^{3 t} (a + \frac{80 - 3 a}{11}) - \frac{e ^{- 8 t} ( 80 - 3 a )}{11}

44 y^{^{'''}} + 15 y^{^{''}} + y^{^{'}} = 0

16 x^{^{''}} + 8 x^{^{'}} + 145 x = 0, x (0) = - 2, x^{^{'}} (0) = 1

y^{^{''}} + 14 y^{^{'}} + 50 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 5, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 13 \frac{d y}{d x} + 12 y = 0