4.7 problem 7

Internal problem ID [4273]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {y^{\prime } x^{2}+y^{2}-y x=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 12

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

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

Solution by Mathematica

Time used: 0.21 (sec). Leaf size: 19

DSolve[x^2*y'[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*}