Internal problem ID [2156]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 9.
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}+y x +y^{2}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 11
dsolve(diff(y(x),x)=(y(x)^2+x*y(x)+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: 0.195 (sec). Leaf size: 13
DSolve[y'[x]==(y[x]^2+x*y[x]+x^2)/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (\log (x)+c_1) \\ \end{align*}