81.6.15 problem 7-15 (a)

Internal problem ID [21561]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-15 (a)
Date solved : Thursday, October 02, 2025 at 07:48:14 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {x^{4}+2 y}{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.140 (sec). Leaf size: 12

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

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