86.2.4 problem 4

Internal problem ID [23078]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:19:07 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 7

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 8

ode=2*x*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 \frac {1}{x^2} \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 7

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

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