60.1.329 problem 336

Internal problem ID [10343]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 336
Date solved : Sunday, March 30, 2025 at 04:14:27 PM
CAS classification : [_exact]

\begin{align*} \left (\sqrt {y^{2}+1}+a x \right ) y^{\prime }+\sqrt {x^{2}+1}+a y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 41

ode:=((1+y(x)^2)^(1/2)+a*x)*diff(y(x),x)+(x^2+1)^(1/2)+a*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {x \sqrt {x^{2}+1}}{2}+\frac {\operatorname {arcsinh}\left (x \right )}{2}+a x y+\frac {y \sqrt {y^{2}+1}}{2}+\frac {\operatorname {arcsinh}\left (y\right )}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.224 (sec). Leaf size: 53

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

\[ \text {Solve}\left [a x y(x)+\frac {1}{2} \left (\text {arcsinh}(y(x))+y(x) \sqrt {y(x)^2+1}\right )+\frac {\text {arcsinh}(x)}{2}+\frac {1}{2} \sqrt {x^2+1} x=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out