4x^{''}+x^'+2x=0,x(0)=0,x(0)=-1,x^'(0)=12

Lösung

4 x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = 0, x (0) = - 1, x^{^{'}} (0) = 12

x = \frac{96}{31} e^{- \frac{t}{8}} sin (\frac{31 t}{8})

Schritte zur Lösung

4 x^{''} (t) + x^{'} (t) + 2 x = 0

Solve linear ODE:

x = \frac{96}{31} e^{- \frac{t}{8}} sin (\frac{31 t}{8})

x = \frac{96}{31} e^{- \frac{t}{8}} sin (\frac{31 t}{8})

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

\frac{d ^{2} y}{d x ^{2}} + 4 (\frac{d y}{d x}) + 4 y = 0

35 y^{^{''''}} + 143 y^{^{''}} + 144 y = 0

y^{^{'''}} - 7 y^{^{''}} + 10 y = 0, y^{^{'}} (0) = 1

7 x^{^{''}} + 3 x^{^{'}} + 7 x = 0, x (0) = - 4, x^{^{'}} (0) = 0