15.6.8 problem 8

Internal problem ID [2965]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 8
Date solved : Sunday, March 30, 2025 at 01:02:23 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-2 x^{4}-2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \left (x^{2}+c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 15

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

\[ y(x)\to x^2 \left (x^2+c_1\right ) \]

✓ Sympy. Time used: 0.238 (sec). Leaf size: 10

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

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