7.5.8 problem 8

Internal problem ID [112]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 8
Date solved : Friday, February 07, 2025 at 07:50:37 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime } x^{2}&=x y+x^{2} {\mathrm e}^{\frac {y}{x}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x)=x*y(x)+x^2*exp(y(x)/x),y(x), singsol=all)
 

\[ y = \ln \left (-\frac {1}{\ln \left (x \right )+c_1}\right ) x \]

✓ Solution by Mathematica

Time used: 0.342 (sec). Leaf size: 18

DSolve[x^2*D[y[x],x]==x*y[x]+x^2*Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \log (-\log (x)-c_1) \]