20.1.23 problem Problem 31

Internal problem ID [3580]
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
Date solved : Monday, January 27, 2025 at 07:45:31 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \end{align*}

✓ Solution by Maple

Time used: 0.009 (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)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}}+x^{3} \textit {\_Z}^{2}+c_{1} -x \right ) x \]

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 24

DSolve[D[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],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x y(x)^2+e^{\frac {y(x)}{x}}-x=c_1,y(x)\right ] \]