15.7.8 problem 8

Internal problem ID [2989]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:05:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 19

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

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