60.2.46 problem 622

Internal problem ID [10620]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 622
Date solved : Sunday, March 30, 2025 at 06:10:53 PM
CAS classification : [[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {1}{y+2+\sqrt {3 x +1}} \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 70

ode:=diff(y(x),x) = 1/(y(x)+2+(3*x+1)^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ -2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (\sqrt {3 x +1}+2 y+4\right ) \sqrt {33}}{11 \sqrt {3 x +1}}\right )+11 \ln \left (\left (3 y+6\right ) \sqrt {3 x +1}+3 y^{2}-6 x +12 y+10\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.216 (sec). Leaf size: 140

ode=D[y[x],x] == (2 + Sqrt[1 + 3*x] + y[x])^(-1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [6 \sqrt {33} \text {arctanh}\left (\frac {3 y(x)+7 \sqrt {3 x+1}+6}{\sqrt {33} \left (y(x)+\sqrt {3 x+1}+2\right )}\right )+44 c_1=33 \left (\log \left (\frac {-3 \sqrt {3 x+1} y(x)^2-3 \left (3 x+4 \sqrt {3 x+1}+1\right ) y(x)+6 x \left (\sqrt {3 x+1}-3\right )-10 \sqrt {3 x+1}-6}{2 (3 x+1)^{3/2}}\right )+\log (12 x+4)\right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(sqrt(3*x + 1) + y(x) + 2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out