88.4.3 problem 3

Internal problem ID [23967]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 33
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:48:00 PM
CAS classification : [_separable]

\begin{align*} x^{2} y+\left (1+x \right ) 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: 19

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

\[ y = \frac {2 \,{\mathrm e}^{-\frac {\left (x -1\right )^{2}}{2}}}{x +1} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.209 (sec). Leaf size: 20

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

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