88.4.8 problem 8

Internal problem ID [23972]
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 : 8
Date solved : Thursday, October 02, 2025 at 09:48:16 PM
CAS classification : [_separable]

\begin{align*} y x +\ln \left (y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 29

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

\begin{align*} y &= {\mathrm e}^{\sqrt {-x^{2}+4}} \\ y &= {\mathrm e}^{-\sqrt {-x^{2}+4}} \\ \end{align*}

✓ Mathematica. Time used: 0.417 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 1.311 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = e^{- \sqrt {4 - x^{2}}}, \ y{\left (x \right )} = e^{\sqrt {4 - x^{2}}}\right ] \]