82.19.5 problem Ex. 5
Internal
problem
ID
[18773]
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, March 13, 2025 at 12:55:21 PM
CAS
classification
:
[[_homogeneous, `class C`], _dAlembert]
\begin{align*} \left (1+y^{\prime }\right )^{3}&=\frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \end{align*}
✓ Maple. Time used: 1.011 (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 \left (x \right ) &= -x \\
y \left (x \right ) &= -x +\operatorname {RootOf}\left (-2 x +\int _{}^{\textit {\_Z}}-\frac {\left (\textit {\_a} \,a^{2}\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 (\textit {\_a} \,a^{2}\right )^{{1}/{3}} \textit {\_a}}d \textit {\_a} +2 c_{1} \right ) \\
y \left (x \right ) &= -x +\operatorname {RootOf}\left (-x -\int _{}^{\textit {\_Z}}\frac {\left (\textit {\_a} \,a^{2}\right )^{{1}/{3}} \left (7 \textit {\_a} +4 a \right )}{i \sqrt {3}\, 14^{{2}/{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 (\textit {\_a} \,a^{2}\right )^{{1}/{3}} \textit {\_a}}d \textit {\_a} +c_{1} \right ) \\
y \left (x \right ) &= -x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {\left (\textit {\_a} \,a^{2}\right )^{{1}/{3}} \left (7 \textit {\_a} +4 a \right )}{i \sqrt {3}\, 14^{{2}/{3}} a \textit {\_a} +a \textit {\_a} 14^{{2}/{3}}+2 i \sqrt {3}\, 14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}-2 \,14^{{1}/{3}} \left (a^{4} \textit {\_a}^{2}\right )^{{1}/{3}}+14 \left (\textit {\_a} \,a^{2}\right )^{{1}/{3}} \textit {\_a}}d \textit {\_a} +c_{1} \right ) \\
\end{align*}
✓ Mathematica. Time used: 155.284 (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]
Too large to display
✗ 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