14.3.16 problem Problem 16

Internal problem ID [3625]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 16
Date solved : Tuesday, September 30, 2025 at 06:48:39 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 13

ode:=diff(y(x),x)+2*y(x)/x = 4*x; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 12

ode=D[y[x],x]+2/x*y[x]==4*x; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+\frac {1}{x^2} \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x + Derivative(y(x), x) + 2*y(x)/x,0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{4} + 1}{x^{2}} \]