xy(dy)/(dx)=x^2+1

解答

x y \frac{d y}{d x} = x^{2} + 1

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

求解步骤

x y \frac{d y}{d x} = x^{2} + 1

求解可分离方程:

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

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

(y - 1) sin (x) d x - d y = 0

\frac{d y}{d x} = 1 + y^{2}, y (0) = 0

\frac{d y}{d x} + 5 x e^{y} = 0

e^{y} y^{^{'}} - x^{2} = 0

y (169 - x^{2})^{\frac{1}{2}} d y = (169 + y^{2})^{\frac{1}{2}} d x