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

Lösung

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

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

Schritte zur Lösung

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

Solve using substitution:

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

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

\frac{d}{d x} ((2 - x)^{3})

\int - \frac{1}{2 x} d x

x \to \frac{π}{3} - lim (cot (3 x))

t an g e n t f (x) = x^{2} - 4, (3, 5)

\frac{d}{d x} (2 x^{6} - 5 x^{- \frac{1}{2}})