9y^{''}-64y=0,y(0)=1,y^'(0)=0

Lösung

9 y^{^{''}} - 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 - \frac{1}{2}) e^{\frac{8 t}{3}} + \frac{1}{2} e^{- \frac{8 t}{3}}

Schritte zur Lösung

9 y^{''} (t) - 64 y = 0

Solve linear ODE:

y = (1 - \frac{1}{2}) e^{\frac{8 t}{3}} + \frac{1}{2} e^{- \frac{8 t}{3}}

y = (1 - \frac{1}{2}) e^{\frac{8 t}{3}} + \frac{1}{2} e^{- \frac{8 t}{3}}

4 y^{^{''}} - y^{^{'}} - 3 y = 0, y (0) = 9, y^{^{'}} (0) = 0.25

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (\frac{1}{3}) = 9, y (0) = 3

x^{^{''}} + 64 x^{^{'}} = 0

3 \frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} - 5 y = 0

y^{^{'}} + y^{^{''}} = y^{^{'''}}