(d^3y)/(dx^3)+5y=0

Lösung

\frac{d ^{3} y}{d x ^{3}} + 5 y = 0

y = c_{1} e^{- 35 x} + e^{\frac{3 5 x}{2}} (c_{2} cos (\frac{3 5 3 x}{2}) + c_{3} sin (\frac{3 5 3 x}{2}))

Schritte zur Lösung

\frac{d ^{3} y}{d x ^{3}} + 5 y = 0

Solve linear ODE:

y = c_{1} e^{- 35 x} + e^{\frac{3 5 x}{2}} (c_{2} cos (\frac{3 5 3 x}{2}) + c_{3} sin (\frac{3 5 3 x}{2}))

y = c_{1} e^{- 35 x} + e^{\frac{3 5 x}{2}} (c_{2} cos (\frac{3 5 3 x}{2}) + c_{3} sin (\frac{3 5 3 x}{2}))

y^{^{''}} + 5 y^{^{'}} - 14 y = 0, y^{^{'}} (0) = 56

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y^{^{'}} (0) = 2, y (0) = 1

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{64}{5}

y^{^{''''}} + 4 y^{^{'''}} + 4 y^{^{''}} = 0

4 y^{^{''}} + 4 y^{^{'}} + 325 y = 0, y (0) = 3, y^{^{'}} (0) = 2