36.2.26 problem 36 part(b)

Internal problem ID [6319]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 36 part(b)
Date solved : Wednesday, March 05, 2025 at 12:34:43 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2} \end{align*}

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

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

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.195 (sec). Leaf size: 12

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

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