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Beliebt Rechnen >

y^{''}+12y^'+36y=0,y(0)=3,y^'(0)=0

Lösung

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0

Lösung

y = 3 e^{- 6 t} + 18 t e^{- 6 t}

Schritte zur Lösung

y^{''} (t) + 12 y^{'} (t) + 36 y = 0

Solve linear ODE:

y = 3 e^{- 6 t} + 18 t e^{- 6 t}

y = 3 e^{- 6 t} + 18 t e^{- 6 t}

Graph

Beliebte Beispiele

{(d^2y)/(dx^2)+4(dy)/(dx)+20y}^2=0

{\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 20 y}^{2} = 0

3y^{'''}+17y^{''}+31y^'+14y=0

3 y^{^{'''}} + 17 y^{^{''}} + 31 y^{^{'}} + 14 y = 0

2y^{''}-3y^'+1/2 y=0

2 y^{^{''}} - 3 y^{^{'}} + \frac{1}{2} y = 0

(d^4y)/(dx^4)-2(d^2y)/(dx^2)+y=0

\frac{d ^{4} y}{d x ^{4}} - 2 \frac{d ^{2} y}{d x ^{2}} + y = 0

(d^2f)/(dx^2)=a^2f(x)

\frac{d ^{2} f}{d x ^{2}} = a^{2} f (x)