65.6.10 problem 10

Internal problem ID [15703]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:23:31 AM
CAS classification : [_separable]

\begin{align*} y-x^{2} y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 12

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

\[ y = {\mathrm e}^{\frac {x -1}{x}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.163 (sec). Leaf size: 10

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

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