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Beliebt Rechnen >

xy^'-2sqrt(y)ln(x)=0

Lösung

x \cdot y^{^{'}} - 2 y \cdot ln (x) = 0

Lösung

y = \frac{ln ^{4} ( x )}{4} + \frac{c _{1} ln ^{2} ( x )}{2} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

x \cdot y^{'} (x) - 2 y \cdot ln (x) = 0

Solve separable ODE:

y = \frac{ln ^{4} ( x )}{4} + \frac{c _{1} ln ^{2} ( x )}{2} + \frac{c _{1}^{2}}{4}

y = \frac{ln ^{4} ( x )}{4} + \frac{c _{1} ln ^{2} ( x )}{2} + \frac{c _{1}^{2}}{4}

Graph

Beliebte Beispiele

(dy)/(dx)=sin(x)e^{2y}

\frac{d y}{d x} = sin (x) e^{2 y}

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

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

2y^4dx+5y^3xdy=0

2 y^{4} d x + 5 y^{3} x d y = 0

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

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

(1 - x^{2}) d y = y d x