Internal problem ID [2165]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`]]
\[ \boxed {2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(2*x*y(x)*diff(y(x),x)-(x^2*exp(-y(x)^2/x^2)+2*y(x)^2)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {\ln \left (\ln \left (x \right )+c_{1} \right )}\, x \\ y \left (x \right ) = -\sqrt {\ln \left (\ln \left (x \right )+c_{1} \right )}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.141 (sec). Leaf size: 38
DSolve[2*x*y[x]*y'[x]-(x^2*Exp[-y[x]^2/x^2]+2*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {\log (\log (x)+2 c_1)} \\ y(x)\to x \sqrt {\log (\log (x)+2 c_1)} \\ \end{align*}