35.4.7 problem 7

Internal problem ID [6125]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:37:31 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve(x^2*diff(y(x),x)+(y(x)^2-x*y(x))=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 19

DSolve[x^2*D[y[x],x]+(y[x]^2-x*y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

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