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Beliebt Rechnen >

(1+e^x)y*y^'=e^x

Lösung

(1 + e^{x}) y \cdot y^{^{'}} = e^{x}

Lösung

y = 2 ln (1 + e^{x}) + c_{1}, y = - 2 ln (1 + e^{x}) + c_{1}

Schritte zur Lösung

(1 + e^{x}) y \cdot y^{'} (x) = e^{x}

Solve separable ODE:

y = 2 ln (1 + e^{x}) + c_{1}, y = - 2 ln (1 + e^{x}) + c_{1}

y = 2 ln (1 + e^{x}) + c_{1}, y = - 2 ln (1 + e^{x}) + c_{1}

Graph

Beliebte Beispiele

(dy)/(dx)=(10(1+x))/(xy)

\frac{d y}{d x} = \frac{10 ( 1 + x )}{x y}

(dx)/(dt)+cos(t)x=cos(t)

\frac{d x}{d t} + cos (t) x = cos (t)

5sqrt(xy)(dy)/(dx)=4,y>0

5 x y \frac{d y}{d x} = 4, y > 0

(dv)/(dt)=sqrt(2/9 v)

\frac{d v}{d t} = \frac{2}{9} v

(dy)/(dx)=4cos(x)sec(y)

\frac{d y}{d x} = 4 cos (x) sec (y)