58.7.1 problem 1

Internal problem ID [14656]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:48:50 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 59

ode:=5*x*y(x)+4*y(x)^2+1+(x^2+2*x*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-x^{3}-\sqrt {x^{6}-x^{4}-4 c_1}}{2 x^{2}} \\ y &= \frac {-x^{3}+\sqrt {x^{6}-x^{4}-4 c_1}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.43 (sec). Leaf size: 84

ode=(5*x*y[x]+4*y[x]^2+1)+(x^2+2*x*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^5+\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4}\\ y(x)&\to -\frac {x}{2}+\frac {\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x*y(x) + (x**2 + 2*x*y(x))*Derivative(y(x), x) + 4*y(x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out