(dy}{dx}=\frac{xarctan(x))/y

解

\frac{d y}{d x} = \frac{x arctan ( x )}{y}

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

解答ステップ

\frac{d y}{d x} = \frac{x arctan ( x )}{y}

分離可能 ODE を解く:

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

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