36y^{''}-81y=0,y(0)=0,y^'(0)=1

Lösung

36 y^{^{''}} - 81 y = 0, y (0) = 0, y^{^{'}} (0) = 1

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

Schritte zur Lösung

36 y^{''} (t) - 81 y = 0

Solve linear ODE:

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

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

\frac{4}{32} y^{^{''}} + 3 y = 0

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y^{^{'}} (\frac{π}{2}) = 12

y^{^{''}} + 6 y^{^{'}} + 2 y = 0, y (0) = 4, y^{^{'}} (0) = 0

100 y^{^{''}} - 140 y^{^{'}} + 74 y = 0, y (3) = 6, y^{^{'}} (3) = 5

y^{^{''}} - 26 y^{^{'}} + 233 y = 0