30.2.20 problem 20

Internal problem ID [7448]
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 : 20
Date solved : Tuesday, September 30, 2025 at 04:35:40 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 18

ode:=diff(y(x),x)+3*y(x)/x+2 = 3*x; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3 x^{2}}{5}-\frac {x}{2}+\frac {9}{10 x^{3}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 29

ode=D[y[x],x]+3*y[x]/x+2==3*x; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\int _1^xK[1]^3 (3 K[1]-2)dK[1]+1}{x^3} \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + Derivative(y(x), x) + 2 + 3*y(x)/x,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\frac {x^{4} \left (6 x - 5\right )}{10} + \frac {9}{10}}{x^{3}} \]