54.2.14 problem 16
Internal
problem
ID
[8546]
Book
:
Elementary
differential
equations.
Rainville,
Bedient,
Bedient.
Prentice
Hall.
NJ.
8th
edition.
1997.
Section
:
CHAPTER
16.
Nonlinear
equations.
Miscellaneous
Exercises.
Page
340
Problem
number
:
16
Date
solved
:
Sunday, March 30, 2025 at 01:17:22 PM
CAS
classification
:
[[_1st_order, _with_linear_symmetries], _dAlembert]
\begin{align*} {y^{\prime }}^{3}-2 x y^{\prime }-y&=0 \end{align*}
✓ Maple. Time used: 0.030 (sec). Leaf size: 442
ode:=diff(y(x),x)^3-2*x*diff(y(x),x)-y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
-\frac {c_1}{{\left (\frac {\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x -\frac {{\left (\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 x \right )}^{2}}{96 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\
-\frac {c_1}{{\left (\frac {i \sqrt {3}\, \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 i \sqrt {3}\, x -\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x +\frac {3 {\left (-\frac {\left (\sqrt {3}+i\right ) \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}}{24}+x \left (-i+\sqrt {3}\right )\right )}^{2}}{2 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\
-\frac {12^{{2}/{3}} c_1}{{\left (\frac {-i \sqrt {3}\, \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 i \sqrt {3}\, x -\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x +\frac {3 {\left (\frac {\left (i-\sqrt {3}\right ) \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}}{24}+\left (\sqrt {3}+i\right ) x \right )}^{2}}{2 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\
\end{align*}
✗ Mathematica
ode=(D[y[x],x])^3-2*x*D[y[x],x]-y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Timed out
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-2*x*Derivative(y(x), x) - y(x) + Derivative(y(x), x)**3,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out