Internal problem ID [5320]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
190
Problem number: 4(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}+x y+y^{2}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve(diff(y(x),x)=(x^2+x*y(x)+y(x)^2)/x^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.2 (sec). Leaf size: 13
DSolve[y'[x]==(x^2+x*y[x]+y[x]^2)/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (\log (x)+c_1) \\ \end{align*}