84.5.11 problem 3.3 (c)

Internal problem ID [22098]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.3 (c)
Date solved : Sunday, October 12, 2025 at 05:52:18 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 1+x y+y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 47

ode:=1+x*y(x)+y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (2^{{2}/{3}} x^{2}-4 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\textit {\_Z} \right ) 2^{{1}/{3}} c_1 x +2^{{1}/{3}} x \operatorname {AiryAi}\left (\textit {\_Z} \right )+2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_1 +2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right )\right ) 2^{{1}/{3}}}{4} \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 121

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

\[ \text {Solve}\left [\frac {(-1)^{2/3} \sqrt [3]{2} x \operatorname {AiryAi}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (x^2+2 y(x)\right )\right )+2 \operatorname {AiryAiPrime}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (x^2+2 y(x)\right )\right )}{(-1)^{2/3} \sqrt [3]{2} x \operatorname {AiryBi}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (x^2+2 y(x)\right )\right )+2 \operatorname {AiryBiPrime}\left (-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \left (x^2+2 y(x)\right )\right )}+c_1=0,y(x)\right ] \]

✗ Sympy

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

NotImplementedError : The given ODE x + Derivative(y(x), x) + 1/y(x) cannot be solved by the factorable group method