60.1.415 problem 426

Internal problem ID [10429]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 426
Date solved : Sunday, March 30, 2025 at 04:41:44 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} \left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \end{align*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 51

ode:=(3*x+1)*diff(y(x),x)^2-3*(2+y(x))*diff(y(x),x)+9 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -2-2 \sqrt {3 x +1} \\ y &= -2+2 \sqrt {3 x +1} \\ y &= \frac {9+\left (3 x +1\right ) c_1^{2}-6 c_1}{3 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 60

ode=9 - 3*(2 + y[x])*D[y[x],x] + (1 + 3*x)*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 \left (x+\frac {1}{3}\right )-2+\frac {3}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \left (\sqrt {3 x+1}+1\right ) \\ y(x)\to 2 \left (\sqrt {3 x+1}-1\right ) \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x + 1)*Derivative(y(x), x)**2 - (3*y(x) + 6)*Derivative(y(x), x) + 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out