Internal problem ID [2100]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 y x^{2}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 21
dsolve(diff(y(x),x)=(x^2*(1-y(x)^2)+y(x)*exp(y(x)/x))/(x*(exp(y(x)/x)+2*x^2*y(x))),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left ({\mathrm e}^{\textit {\_Z}}+x^{3} \textit {\_Z}^{2}+c_{1}-x \right ) x \]
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 24
DSolve[y'[x]==(x^2*(1-y[x]^2)+y[x]*Exp[y[x]/x])/(x*(Exp[y[x]/x]+2*x^2*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x y(x)^2+e^{\frac {y(x)}{x}}-x=c_1,y(x)\right ] \]