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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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\frac{\partial}{\partial x} (x^{2} cos (x) y)

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