xyy^'=-(1+x^2)

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{- y + 10} = \frac{d x}{x + 1}

x y^{^{'}} - y = 2 x^{3} y

\frac{d y}{d t} = \frac{t + 1}{t y}, y (1) = - 3

y^{^{'}} + 4 y = 1.4

y^{^{'}} - y = 2