84.13.4 problem 7.5
Internal
problem
ID
[22154]
Book
:
Schaums
outline
series.
Differential
Equations
By
Richard
Bronson.
1973.
McGraw-Hill
Inc.
ISBN
0-07-008009-7
Section
:
Chapter
7.
Integrating
factors.
Solved
problems.
Page
29
Problem
number
:
7.5
Date
solved
:
Thursday, October 02, 2025 at 08:32:50 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \end{align*}
✓ Maple. Time used: 0.098 (sec). Leaf size: 26
ode:=diff(y(x),x) = 3*y(x)*x^2/(x^3+2*y(x)^4);
dsolve(ode,y(x), singsol=all);
\[
y = \operatorname {RootOf}\left (2 x^{9} \textit {\_Z}^{4}-3-{\mathrm e}^{\frac {9 c_1}{4}} \textit {\_Z} \right ) x^{3}
\]
✓ Mathematica. Time used: 60.071 (sec). Leaf size: 891
ode=D[y[x],x]==(3*y[x]*x^2)/(x^3+2*y[x]^4);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {1}{4} \left (-\sqrt {2} \sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}-2 \sqrt {-\frac {1}{2} \sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}+\frac {4 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}-\frac {3 \sqrt {2} c_1}{\sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}}}\right )\\ y(x)&\to \frac {1}{4} \left (2 \sqrt {-\frac {1}{2} \sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}+\frac {4 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}-\frac {3 \sqrt {2} c_1}{\sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}}}-\sqrt {2} \sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}\right )\\ y(x)&\to \frac {1}{4} \left (\sqrt {2} \sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}-2 \sqrt {-\frac {1}{2} \sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}+\frac {4 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}+\frac {3 \sqrt {2} c_1}{\sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}}}\right )\\ y(x)&\to \frac {1}{4} \left (\sqrt {2} \sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}+2 \sqrt {-\frac {1}{2} \sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}+\frac {4 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}+\frac {3 \sqrt {2} c_1}{\sqrt {\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}-\frac {8 x^3}{\sqrt [3]{\sqrt {512 x^9+81 c_1{}^4}+9 c_1{}^2}}}}}\right ) \end{align*}
✓ Sympy. Time used: 1.078 (sec). Leaf size: 1057
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-3*x**2*y(x)/(x**3 + 2*y(x)**4) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\text {Solution too large to show}
\]