2y^{''}+5y^'-3y=0,y(0)=3,y^'(0)=16

Lösung

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 3, y^{^{'}} (0) = 16

y = (3 + \frac{29}{7}) e^{\frac{t}{2}} - \frac{29}{7} e^{- 3 t}

Schritte zur Lösung

2 y^{''} (t) + 5 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = (3 + \frac{29}{7}) e^{\frac{t}{2}} - \frac{29}{7} e^{- 3 t}

y = (3 + \frac{29}{7}) e^{\frac{t}{2}} - \frac{29}{7} e^{- 3 t}

\frac{3}{4} x^{^{''}} + 192 x = 0, x (0) = - \frac{1}{4}, x^{^{'}} (0) = 0

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

\frac{1}{2} x^{^{''}} + 25 x = 0

3 y^{^{''}} - 24 y^{^{'}} = - 48 y

3 y^{^{''}} + 48 y = 0, y (0) = 3, y^{^{'}} (0) = 20