9y^{''}-12y+4y=0

Lösung

9 y^{^{''}} - 12 y + 4 y = 0

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

Schritte zur Lösung

9 y^{''} (t) - 12 y + 4 y = 0

Solve linear ODE:

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

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

2 y^{^{''}} + 36 y^{^{'}} + 163 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} - 9 y = 0, y (1) = 1

x^{^{''}} + 2 x^{^{'}} + 3 x = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = 10

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = 0