35.3.6 problem 6

Internal problem ID [6110]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 6
Date solved : Sunday, March 30, 2025 at 10:39:03 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x)+y(x)/(x^2+1)^(1/2) = 1/(x+(x^2+1)^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x +c_1}{x +\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 23

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

\[ y(x)\to \left (\sqrt {x^2+1}-x\right ) (x+c_1) \]

✗ Sympy

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

Timed Out