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Beliebt Rechnen >

(dy)/(dx)y=(2x)/(1+x^2)

Lösung

\frac{d y}{d x} y = \frac{2 x}{1 + x ^{2}}

Lösung

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

Schritte zur Lösung

\frac{d y}{d x} y = \frac{2 x}{1 + x ^{2}}

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(dx)/(dt)=x(1+t^2)

\frac{d x}{d t} = x (1 + t^{2})

(dy)/(dx)=3x^2y-y

\frac{d y}{d x} = 3 x^{2} y - y

x^2(dy)/(dx)-y^2=1

x^{2} \frac{d y}{d x} - y^{2} = 1

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

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

(dv)/(dt)+v+v^2=0

\frac{d v}{d t} + v + v^{2} = 0