Internal problem ID [2199]
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 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 y}{x}-y^{2}+\frac {2}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 24
dsolve(diff(y(x),x)+2/x*y(x)-y(x)^2=-2/x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}+2 c_{1}}{\left (-x^{3}+c_{1}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 35
DSolve[y'[x]+2/x*y[x]-y[x]^2==-2/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2+3 c_1 x^3}{x-3 c_1 x^4} \\ y(x)\to -\frac {1}{x} \\ \end{align*}