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Beliebt Rechnen >

2y^{'''}+7y^{''}+4y^'-4y=0

Lösung

2 y^{^{'''}} + 7 y^{^{''}} + 4 y^{^{'}} - 4 y = 0

Lösung

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- 2 t} + c_{3} t e^{- 2 t}

Schritte zur Lösung

2 y^{'''} (t) + 7 y^{''} (t) + 4 y^{'} (t) - 4 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- 2 t} + c_{3} t e^{- 2 t}

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- 2 t} + c_{3} t e^{- 2 t}

Graph

Beliebte Beispiele

y^{''}+25y^'+2500y=0

y^{^{''}} + 25 y^{^{'}} + 2500 y = 0

3y^{''}-2y+4y^'=0

3 y^{^{''}} - 2 y + 4 y^{^{'}} = 0

y^'x+(y^{''})/2 x=0

y^{^{'}} x + \frac{y ^{^{''}}}{2} x = 0

y^{''}-7y^{''}+19y^'-13y=0

y^{^{''}} - 7 y^{^{''}} + 19 y^{^{'}} - 13 y = 0

(d^2y)/(dx^2)+2a(dy)/(dx)+(b^2)y=0

\frac{d ^{2} y}{d x ^{2}} + 2 a \frac{d y}{d x} + (b^{2}) y = 0