80.3.29 problem 30

Internal problem ID [21193]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 30
Date solved : Thursday, October 02, 2025 at 07:16:43 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

ode:=x^2+a__1*x*y(x)+a__2*y(x)^2+(x^2+b__1*x*y(x)+b__2*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2} b_{2} +\textit {\_a} b_{1} +1}{\textit {\_a}^{3} b_{2} +\textit {\_a}^{2} a_{2} +\textit {\_a}^{2} b_{1} +\textit {\_a} a_{1} +\textit {\_a} +1}d \textit {\_a} +\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 110

ode=(x^2+a1*x*y[x]+a2*y[x]^2)+(x^2+b1*x*y[x]+b2*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {b2}+\text {$\#$1}^2 \text {a2}+\text {$\#$1}^2 \text {b1}+\text {$\#$1} \text {a1}+\text {$\#$1}+1\&,\frac {\text {$\#$1}^2 \text {b2} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+\text {$\#$1} \text {b1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2 \text {b2}+2 \text {$\#$1} \text {a2}+2 \text {$\#$1} \text {b1}+\text {a1}+1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a1 = symbols("a1") 
a2 = symbols("a2") 
b1 = symbols("b1") 
b2 = symbols("b2") 
y = Function("y") 
ode = Eq(a1*x*y(x) + a2*y(x)**2 + x**2 + (b1*x*y(x) + b2*y(x)**2 + x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out