1/x y^'= y/(x^2)-1/y

Lösung

\frac{1}{x} y^{^{'}} = \frac{y}{x ^{2}} - \frac{1}{y}

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

Schritte zur Lösung

\frac{1}{x} y^{'} (x) = \frac{y}{x ^{2}} - \frac{1}{y}

Solve Bernoulli ODE:

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

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

\frac{\partial}{\partial y} (y^{3} + x^{2} y - 3 y)

n = 1 \sum \infty \frac{1}{n ln ( n )}

\int \frac{cos ( θ )}{9 - sin ^{2} ( θ )} d θ

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

t an g e n t f (x) = 5 x^{3} - 5 x, at x = - 1