83.10.5 problem 5

Internal problem ID [21974]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter IV. First order differential equations of higher degree. Ex. XI at page 69
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:20:54 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 59

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

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

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out