20.4.45 problem Problem 63

Internal problem ID [3680]
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
Date solved : Monday, January 27, 2025 at 07:54:40 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} y^{\prime }+\frac {7 y}{x}-3 y^{2}&=\frac {3}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(x),x)+7/x*y(x)-3*y(x)^2=3/x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 15

DSolve[D[y[x],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*}