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Beliebt Rechnen >

(1+x^2)((dy)/(dx))+xe^{-y}=0

Lösung

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

Lösung

y = ln (- \frac{1}{2} ln (1 + x^{2}) + c_{1})

Schritte zur Lösung

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

Solve separable ODE:

y = ln (- \frac{1}{2} ln (1 + x^{2}) + c_{1})

y = ln (- \frac{1}{2} ln (1 + x^{2}) + c_{1})

Graph

Beliebte Beispiele

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

x^2(y^')^1-3xy^'+16y=0

x^{2} (y^{^{'}})^{1} - 3 x y^{^{'}} + 16 y = 0

(dy)/(dx)=100-y/(100)

\frac{d y}{d x} = 100 - \frac{y}{100}

(dy}{dx}=\frac{(y^2))/x ,y(1)= 1/3

\frac{d y}{d x} = \frac{( y ^{2} )}{x}, y (1) = \frac{1}{3}

y'(t)=y(y+1)^2,y(0)=1.2

y^{'} (t) = y (y + 1)^{2}, y (0) = 1.2