8.5.8 problem 8

Internal problem ID [736]
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
Date solved : Monday, January 27, 2025 at 03:00:16 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.300 (sec). Leaf size: 18

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

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