(dy)/(dx)-(5y)/(x^2)= 1/(x^2)

Lösung

\frac{d y}{d x} - \frac{5 y}{x ^{2}} = \frac{1}{x ^{2}}

y = \frac{e ^{\frac{- 5 + 5 c _{1} x}{x}}}{5} - \frac{1}{5}

Schritte zur Lösung

\frac{d y}{d x} - \frac{5 y}{x ^{2}} = \frac{1}{x ^{2}}

Solve separable ODE:

y = \frac{e ^{\frac{- 5 + 5 c _{1} x}{x}}}{5} - \frac{1}{5}

y = \frac{e ^{\frac{- 5 + 5 c _{1} x}{x}}}{5} - \frac{1}{5}

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

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

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

y^{^{'}} = sin (3 y)

\frac{d y}{d x} = e^{5 y} cos (\frac{x}{2})