29.7.18 problem 193

Internal problem ID [4793]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 193
Date solved : Sunday, March 30, 2025 at 03:55:08 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: 27

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: 60.245 (sec). Leaf size: 2509

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: 0.643 (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)
 

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