Internal problem ID [4781]
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]
\[ \boxed {x^{2} y^{\prime }+y^{2}-x y=0} \]
✓ 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)
\[ y \left (x \right ) = \frac {x}{\ln \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.132 (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*}