Internal problem ID [11612]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises
page 37
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}+2 y x -x^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((y(x)^2+2*x*y(x))-x^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{c_{1} -x} \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 23
DSolve[(y[x]^2+2*x*y[x])-x^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{x-c_1} \\ y(x)\to 0 \\ \end{align*}