82.12.10 problem Ex. 10

Internal problem ID [18775]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 10
Date solved : Tuesday, January 28, 2025 at 12:16:47 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[x*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*}