89.6.22 problem 22

Internal problem ID [24405]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 22
Date solved : Thursday, October 02, 2025 at 10:25:38 PM
CAS classification : [_exact, _rational]

\begin{align*} 3-2 y x -\left (x^{2}+\frac {1}{y^{2}}+\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 31

ode:=3-2*x*y(x)-(x^2+1/y(x)^2+1/y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-x^{2} {\mathrm e}^{2 \textit {\_Z}}+c_1 \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+3 x \,{\mathrm e}^{\textit {\_Z}}+1\right )} \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 25

ode=(3-2*x*y[x] )-(x^2+1/y[x]^2+1/y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^2 y(x)-\frac {1}{y(x)}+\log (y(x))-3 x=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) - (x**2 + 1/y(x) + y(x)**(-2))*Derivative(y(x), x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out