73.7.11 problem 11

Internal problem ID [15098]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 11
Date solved : Monday, March 31, 2025 at 01:24:25 PM
CAS classification : [_linear]

\begin{align*} 3 y-x^{3}+x y^{\prime }&=0 \end{align*}

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

ode:=3*y(x)-x^3+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{6}+6 c_1}{6 x^{3}} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 19

ode=3*y[x]-x^3+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^3}{6}+\frac {c_1}{x^3} \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{6}}{6}}{x^{3}} \]