20.4.44 problem Problem 62

Internal problem ID [3679]
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
Date solved : Monday, January 27, 2025 at 07:54:37 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }+\frac {2 y}{x}-y^{2}&=-\frac {2}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 2.898 (sec). Leaf size: 24

dsolve(diff(y(x),x)+2/x*y(x)-y(x)^2=-2/x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{3}+2 c_{1}}{\left (-x^{3}+c_{1} \right ) x} \]

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 35

DSolve[D[y[x],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*}