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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

d y = (y + 1) (1 - x) d x, f (1) = 0

\frac{d S}{d t} = 2 - \frac{S}{10}

x^{\frac{1}{2}} d y - y^{- \frac{3}{2}} d x = 0

x y + y^{^{'}} = 84 x

\frac{d y}{d t} = 20 y