23.1.199 problem 196 (b)

Internal problem ID [4806]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 196 (b)
Date solved : Tuesday, September 30, 2025 at 08:41:22 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ \ln \left (x \right )+\int _{}^{y}\frac {1}{2 \textit {\_a} +\sqrt {\textit {\_a}^{2}+1}}d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 60.122 (sec). Leaf size: 2149

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

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✓ Sympy. Time used: 0.347 (sec). Leaf size: 31

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

\[ \log {\left (x \right )} + \frac {2 \log {\left (\sqrt {y^{2}{\left (x \right )} + 1} + 2 y{\left (x \right )} \right )}}{3} - \frac {\operatorname {asinh}{\left (y{\left (x \right )} \right )}}{3} = C_{1} \]