Internal problem ID [86]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-{\mathrm e}^{\frac {y}{x}} x^{2}-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x) = exp(y(x)/x)*x^2+x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \ln \left (-\frac {1}{\ln \relax (x )+c_{1}}\right ) x \]
✓ Solution by Mathematica
Time used: 0.309 (sec). Leaf size: 18
DSolve[x^2*y'[x] == Exp[y[x]/x]*x^2+x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \log (-\log (x)-c_1) \\ \end{align*}