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Beliebt Rechnen >

(x+1)^2y^'+8(x+1)y^'+12y=0

Lösung

(x + 1)^{2} y^{^{'}} + 8 (x + 1) y^{^{'}} + 12 y = 0

Lösung

y = e^{- 12 (\frac{1}{8} l n (x + 1) - \frac{1}{8} l n (x + 9)) + c_{1}}

Schritte zur Lösung

(x + 1)^{2} y^{'} (x) + 8 (x + 1) y^{'} (x) + 12 y = 0

Solve separable ODE:

y = e^{- 12 (\frac{1}{8} l n (x + 1) - \frac{1}{8} l n (x + 9)) + c_{1}}

y = e^{- 12 (\frac{1}{8} l n (x + 1) - \frac{1}{8} l n (x + 9)) + c_{1}}

Graph

Beliebte Beispiele

derivative of x^2+y^2= derivative of 16

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (16)

(dy)/(dx)=(-0.1)/(cos(y)),y(0)= pi/3

\frac{d y}{d x} = \frac{- 0.1}{cos ( y )}, y (0) = \frac{π}{3}

(dy)/(dx)=y(x^2+5)

\frac{d y}{d x} = y (x^{2} + 5)

y^{^{'}} - 12 x y = 9 x

e^xydy-(e^{-y}+2e^{2x-y})dx=0

e^{x} y d y - (e^{- y} + 2 e^{2 x - y}) d x = 0