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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- x} + c_{2} x e^{- x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x}

y = c_{1} e^{- x} + c_{2} x e^{- x}

Graph

Beliebte Beispiele

y^{''}-4y^'+4y=0,y(0)=1,y^'(0)=5

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 5

y^{''''}+10y^{''}+25y=0

y^{^{''''}} + 10 y^{^{''}} + 25 y = 0

9y^{'''}+11y^{''}+4y^'-14y=0

9 y^{^{'''}} + 11 y^{^{''}} + 4 y^{^{'}} - 14 y = 0

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

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

y^{''}-2y^'-y=0

y^{^{''}} - 2 y^{^{'}} - y = 0