76.19.5 problem Ex. 5

Internal problem ID [20137]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 43
Problem number : Ex. 5
Date solved : Thursday, October 02, 2025 at 05:32:37 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \left (y^{\prime }+1\right )^{3}&=\frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \end{align*}

✓ Maple. Time used: 0.909 (sec). Leaf size: 262

ode:=(1+diff(y(x),x))^3 = 7/4/a*(x+y(x))*(1-diff(y(x),x))^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x \\ y &= -x +\operatorname {RootOf}\left (-2 x +\int _{}^{\textit {\_Z}}-\frac {\left (a^{2} \textit {\_a} \right )^{{1}/{3}} \left (7 \textit {\_a} +4 a \right )}{a \textit {\_a} 14^{{2}/{3}}-2 \,14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}-7 \left (a^{2} \textit {\_a} \right )^{{1}/{3}} \textit {\_a}}d \textit {\_a} +2 c_1 \right ) \\ y &= -x +\operatorname {RootOf}\left (-x -\int _{}^{\textit {\_Z}}\frac {\left (a^{2} \textit {\_a} \right )^{{1}/{3}} \left (7 \textit {\_a} +4 a \right )}{i 14^{{2}/{3}} \sqrt {3}\, a \textit {\_a} +2 i \sqrt {3}\, 14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}-a \textit {\_a} 14^{{2}/{3}}+2 \,14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}-14 \left (a^{2} \textit {\_a} \right )^{{1}/{3}} \textit {\_a}}d \textit {\_a} +c_1 \right ) \\ y &= -x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {\left (a^{2} \textit {\_a} \right )^{{1}/{3}} \left (7 \textit {\_a} +4 a \right )}{a \textit {\_a} 14^{{2}/{3}}+i 14^{{2}/{3}} \sqrt {3}\, a \textit {\_a} -2 \,14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}+14 \left (a^{2} \textit {\_a} \right )^{{1}/{3}} \textit {\_a} +2 i \sqrt {3}\, 14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}}d \textit {\_a} +c_1 \right ) \\ \end{align*}

✓ Mathematica. Time used: 111.629 (sec). Leaf size: 54117

ode=(1+D[y[x],x])^3==2/8*7/a*(x+y[x])*(1-D[y[x],x])^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq((Derivative(y(x), x) + 1)**3 - 7*(1 - Derivative(y(x), x))**3*(x + y(x))/(4*a),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out