(d^4y)/(dx^4)+y=0

Lösung

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

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2}))

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2}))

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2}))

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

y^{^{'''}} + y^{^{''}} + y^{^{'}} = 0

4 \frac{d ^{2} y}{d x ^{2}} + 64 y = 0

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

y^{^{''}} - 11 y = 0