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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

Graph

Beliebte Beispiele

6y^{''}+17y^'-3y=0

6 y^{^{''}} + 17 y^{^{'}} - 3 y = 0

y^{''}-15y^'+56y=0

y^{^{''}} - 15 y^{^{'}} + 56 y = 0

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

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

y^{''}+2y^'+4y=0,y(0)=1,y^'(0)=-2

y^{^{''}} + 2 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

y^{'''}-5y^{''}+7y^'-3y=0

y^{^{'''}} - 5 y^{^{''}} + 7 y^{^{'}} - 3 y = 0