84.16.5 problem 8.14

Internal problem ID [22185]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.14
Date solved : Thursday, October 02, 2025 at 08:33:43 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

ode:=diff(y(x),x)+2*y(x)/x = x; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 17

ode=D[y[x],x]+2/x*y[x]==x; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^4-1}{4 x^2} \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 14

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

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