54.1.521 problem 534

Internal problem ID [11835]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 534
Date solved : Tuesday, September 30, 2025 at 11:16:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+3 y-x&=0 \end{align*}

✓ Maple. Time used: 0.085 (sec). Leaf size: 84

ode:=4*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+3*y(x)-x = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.726 (sec). Leaf size: 79

ode=-x + 3*y[x] - 6*y[x]*D[y[x],x]^2 + 4*x*D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x)**3 - x - 6*y(x)*Derivative(y(x), x)**2 + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out