83.10.6 problem 6
Internal
problem
ID
[21975]
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
:
6
Date
solved
:
Thursday, October 02, 2025 at 08:20:55 PM
CAS
classification
:
[_separable]
\begin{align*} 2 a \,x^{3} y-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \end{align*}
✓ Maple. Time used: 0.032 (sec). Leaf size: 430
ode:=2*a*x^3*y(x)-a*x^2*diff(y(x),x)+c*diff(y(x),x)^3 = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
\frac {-\int _{}^{y}\frac {{\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{2}/{3}}+a {\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{1}/{3}}+a^{2}}{\textit {\_a} {\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{1}/{3}}}d \textit {\_a} +\left (3 x^{2}-6 c_1 \right ) a}{6 a} &= 0 \\
\frac {\int _{}^{y}\frac {i \left ({\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{2}/{3}}-a^{2}\right ) \sqrt {3}+{\left ({\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{1}/{3}}-a \right )}^{2}}{\textit {\_a} {\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{1}/{3}}}d \textit {\_a} +6 \left (x^{2}-2 c_1 \right ) a}{12 a} &= 0 \\
\frac {-\int _{}^{y}\frac {i \left ({\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{2}/{3}}-a^{2}\right ) \sqrt {3}-{\left ({\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{1}/{3}}-a \right )}^{2}}{\textit {\_a} {\left (\left (6 \sqrt {3}\, \sqrt {-c \left (-27 c \,\textit {\_a}^{2}+a \right )}\, \textit {\_a} -54 c \,\textit {\_a}^{2}+a \right ) a^{2}\right )}^{{1}/{3}}}d \textit {\_a} +6 \left (x^{2}-2 c_1 \right ) a}{12 a} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 179.708 (sec). Leaf size: 14400
ode=2*a*x^3*y[x]-a*x^2*D[y[x],x]+c*D[y[x],x]^3==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
c = symbols("c")
y = Function("y")
ode = Eq(2*a*x**3*y(x) - a*x**2*Derivative(y(x), x) + c*Derivative(y(x), x)**3,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out