58.3.3 problem 3

Internal problem ID [14555]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:38:49 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

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

\begin{align*} y &= -\frac {x^{2}}{4}-\frac {\sqrt {x^{4}-8 c_1 -8 x}}{4} \\ y &= -\frac {x^{2}}{4}+\frac {\sqrt {x^{4}-8 c_1 -8 x}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 61

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

\begin{align*} y(x)&\to \frac {1}{4} \left (-x^2-\sqrt {x^4-8 x+16 c_1}\right )\\ y(x)&\to \frac {1}{4} \left (-x^2+\sqrt {x^4-8 x+16 c_1}\right ) \end{align*}

✗ Sympy

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

Timed Out