8.5.9 problem 9

Internal problem ID [737]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 9
Date solved : Monday, January 27, 2025 at 03:00:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {x}{-\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}