3y^{''}-4y=0

Lösung

3 y^{^{''}} - 4 y = 0

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{2 t}{3}}

Schritte zur Lösung

3 y^{''} (t) - 4 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{2 t}{3}}

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{2 t}{3}}

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} = 0

y^{^{'}} = 2 y^{^{''}}

y^{^{'''}} - 5 y^{^{''}} = 0

(D^{3} + 3 D^{2} + 3 D + 1) y = 0

y^{^{'''}} + 5 y^{^{''}} - 32 y^{^{'}} + 36 y = 0