(dy)/(dx)+xy= x/y

Lösung

\frac{d y}{d x} + x y = \frac{x}{y}

y = - e^{- x^{2} - c_{1}} + 1, y = - - e^{- x^{2} - c_{1}} + 1

Schritte zur Lösung

\frac{d y}{d x} + x y = \frac{x}{y}

Solve separable ODE:

y = - e^{- x^{2} - c_{1}} + 1, y = - - e^{- x^{2} - c_{1}} + 1

y = - e^{- x^{2} - c_{1}} + 1, y = - - e^{- x^{2} - c_{1}} + 1

x^{^{'}} = \frac{x ^{2} + x}{2 x + 1}

(2 x^{3} - 1) d x - y d y = 0

(x - 1) d x - (x e^{y} + e^{y}) d y = 0

y^{^{'}} = k \frac{x}{y}

\frac{d y}{d t} - y = 0, y (0) = 1