Internal problem ID [2200]
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 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {7 y}{x}-3 y^{2}-\frac {3}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve(diff(y(x),x)+7/x*y(x)-3*y(x)^2=3/x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \ln \relax (x )-3 c_{1}-1}{3 x \left (\ln \relax (x )-c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 15
DSolve[y'[x]+7/x*y[x]-3*y[x]^2==3/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}