49.21.2 problem 1(b)

Internal problem ID [7732]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 1(b)
Date solved : Wednesday, March 05, 2025 at 04:51:36 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=y(x)*diff(y(x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {x^{2}+c_{1}} \\ y &= -\sqrt {x^{2}+c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 35

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

\begin{align*} y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.299 (sec). Leaf size: 22

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} + x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} + x^{2}}\right ] \]