(d^3+3d^2+3d+1)y=0

Lösung

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

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x}

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x}

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''''}} - 38 y^{^{'''}} + 361 y^{^{''}} = 0

\frac{d ^{4} y}{d x ^{4}} + 5 \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

4 y^{^{''}} + y^{^{'}} = 0, y^{^{'}} (0) = 1, y (0) = 3

y^{^{''}} + 64 y = 0, y (0) = 8, y^{^{'}} (0) = - \frac{4}{3}