23.1.714 problem 710
Internal
problem
ID
[5321]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
1.
THE
DIFFERENTIAL
EQUATION
IS
OF
FIRST
ORDER
AND
OF
FIRST
DEGREE,
page
223
Problem
number
:
710
Date
solved
:
Tuesday, September 30, 2025 at 12:29:38 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} \left (x^{3}-y^{4}\right ) y^{\prime }&=3 x^{2} y \end{align*}
✓ Maple. Time used: 0.024 (sec). Leaf size: 25
ode:=(x^3-y(x)^4)*diff(y(x),x) = 3*x^2*y(x);
dsolve(ode,y(x), singsol=all);
\[
y = \operatorname {RootOf}\left (x^{9} \textit {\_Z}^{4}+3-{\mathrm e}^{\frac {9 c_1}{4}} \textit {\_Z} \right ) x^{3}
\]
✓ Mathematica. Time used: 60.086 (sec). Leaf size: 1021
ode=(x^3-y[x]^4)D[y[x],x]==3 x^2 y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}-\frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}-\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}}\\ y(x)&\to \frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}+\frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}-\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}}\\ y(x)&\to -\frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}-\frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}+\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}}\\ y(x)&\to \frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}+\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}}-\frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}} \end{align*}
✓ Sympy. Time used: 1.207 (sec). Leaf size: 1034
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-3*x**2*y(x) + (x**3 - y(x)**4)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\text {Solution too large to show}
\]