73.7.8 problem 8

Internal problem ID [15087]
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 : 8
Date solved : Thursday, March 13, 2025 at 05:37:10 AM
CAS classification : [_linear]

\begin{align*} 4 x y-6+x^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=4*x*y(x)-6+x^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x^{3}+c_{1}}{x^{4}} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 17

ode=4*x*y[x]-6+x^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 x^3+c_1}{x^4} \]

✓ Sympy. Time used: 0.201 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + 4*x*y(x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\frac {C_{1}}{x^{3}} + 2}{x} \]