73.7.1 problem 1

Internal problem ID [15088]
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 : 1
Date solved : Monday, March 31, 2025 at 01:23:15 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=2 y-6 x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x*diff(y(x),x) = 2*y(x)-6*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2}-6 x^{3} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 15

ode=x*D[y[x],x]==2*y[x]-6*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 (-6 x+c_1) \]

✓ Sympy. Time used: 0.248 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**3 + x*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} - 6 x\right ) \]