81.4.11 problem 5-12

Internal problem ID [21525]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-12
Date solved : Thursday, October 02, 2025 at 07:46:48 PM
CAS classification : [_linear]

\begin{align*} 2 y-8 x^{2}+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

ode:=2*y(x)-8*x^2+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x^{4}+c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {2 x^4+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**2 + x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 2 x^{4}}{x^{2}} \]