83.2.6 problem 2 (a)

Internal problem ID [21917]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. III at page 35
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 08:09:34 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 13

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

\[ y = \sqrt {-x^{2}+5} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to \sqrt {5-x^2} \end{align*}

✓ Sympy. Time used: 0.221 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \sqrt {5 - x^{2}} \]