-3y^{''}+27y=0,y^'(-2)=-2,y(2)=-2

Lösung

- 3 y^{^{''}} + 27 y = 0, y^{^{'}} (- 2) = - 2, y (2) = - 2

y = \frac{( - 2 e ^{6} ( e ^{24} + 1 ) + e ^{12} ( - 6 e ^{6} + 2 e ^{18} ) ) e ^{3 t}}{3 ( e ^{24} + 1 )} + \frac{- 6 e ^{6} + 2 e ^{18}}{3 ( e ^{24} + 1 )} e^{- 3 t}

Schritte zur Lösung

- 3 y^{''} (t) + 27 y = 0

Solve linear ODE:

y = \frac{( - 2 e ^{6} ( e ^{24} + 1 ) + e ^{12} ( - 6 e ^{6} + 2 e ^{18} ) ) e ^{3 t}}{3 ( e ^{24} + 1 )} + \frac{- 6 e ^{6} + 2 e ^{18}}{3 ( e ^{24} + 1 )} e^{- 3 t}

y = \frac{( - 2 e ^{6} ( e ^{24} + 1 ) + e ^{12} ( - 6 e ^{6} + 2 e ^{18} ) ) e ^{3 t}}{3 ( e ^{24} + 1 )} + \frac{- 6 e ^{6} + 2 e ^{18}}{3 ( e ^{24} + 1 )} e^{- 3 t}

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = - 11, y^{^{'}} (0) = 35

12 y^{^{''}} - 11 y^{^{'}} + 2 y = 0, y (0) = 7, y^{^{'}} (0) = - 3

y^{^{''''}} - 4 y^{^{'''}} + 9 y^{^{''}} - 36 y^{^{'}} = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

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