54.1.533 problem 546

Internal problem ID [11847]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 546
Date solved : Tuesday, September 30, 2025 at 11:25:21 PM
CAS classification : [_dAlembert]

\begin{align*} {y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x&=0 \end{align*}

✓ Maple. Time used: 0.071 (sec). Leaf size: 149

ode:=diff(y(x),x)^4+3*(x-1)*diff(y(x),x)^2-3*(2*y(x)-1)*diff(y(x),x)+3*x = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{6}+x \\ y &= \frac {5}{6}-x \\ y &= \frac {\left (3-c_1^{3}+\left (-5 x +3\right ) c_1 \right ) \sqrt {c_1^{2}+4 x}-c_1^{4}+\left (-7 x +3\right ) c_1^{2}+3 c_1 -8 x^{2}}{6 c_1 +6 \sqrt {c_1^{2}+4 x}} \\ y &= \frac {\left (-3+c_1^{3}+\left (5 x -3\right ) c_1 \right ) \sqrt {c_1^{2}+4 x}-c_1^{4}+\left (-7 x +3\right ) c_1^{2}+3 c_1 -8 x^{2}}{6 c_1 -6 \sqrt {c_1^{2}+4 x}} \\ \end{align*}

✓ Mathematica. Time used: 0.293 (sec). Leaf size: 77

ode=3*x - 3*(-1 + 2*y[x])*D[y[x],x] + 3*(-1 + x)*D[y[x],x]^2 + D[y[x],x]^4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{12} \left (-6 c_1 (x-1)-\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6-c_1{}^3\right )\\ y(x)&\to \frac {1}{12} \left (-6 c_1 (x-1)+\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6-c_1{}^3\right ) \end{align*}

✗ Sympy

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

Timed Out