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Beliebt Rechnen >

(xdx)/((1+x))=(dy)/(y^3)

Lösung

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

Lösung

y = - \frac{1}{2 ( x + 1 - ln ( 1 + x ) + c _{1} )}, y = - - \frac{1}{2 ( x + 1 - ln ( 1 + x ) + c _{1} )}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{1}{2 ( x + 1 - ln ( 1 + x ) + c _{1} )}, y = - - \frac{1}{2 ( x + 1 - ln ( 1 + x ) + c _{1} )}

y = - \frac{1}{2 ( x + 1 - ln ( 1 + x ) + c _{1} )}, y = - - \frac{1}{2 ( x + 1 - ln ( 1 + x ) + c _{1} )}

Graph

Beliebte Beispiele

y^'-2yy^'+e^x=0

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

xe^{(x^2)}+yy^'=0

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

y^'=e^{-5y}(2sqrt(7x)-4),y(0)=1

y^{^{'}} = e^{- 5 y} (2 7 x - 4), y (0) = 1

y^'=(y^2+3)/((2xy))

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

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

e^{2 x} \frac{d y}{d x} = \frac{2}{y}