88.8.11 problem 11
Internal
problem
ID
[24019]
Book
:
Elementary
Differential
Equations.
By
Lee
Roy
Wilcox
and
Herbert
J.
Curtis.
1961
first
edition.
International
texbook
company.
Scranton,
Penn.
USA.
CAT
number
61-15976
Section
:
Chapter
2.
Differential
equations
of
first
order.
Exercise
at
page
44
Problem
number
:
11
Date
solved
:
Thursday, October 02, 2025 at 09:54:20 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} y+2 x^{3}+\left (2 x -\frac {x^{4}}{y}\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.020 (sec). Leaf size: 25
ode:=y(x)+2*x^3+(2*x-x^4/y(x))*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = x^{2} c_1 \operatorname {RootOf}\left (x \,\textit {\_Z}^{7}-7 c_1 \,\textit {\_Z}^{5}+x \right )^{5}
\]
✓ Mathematica. Time used: 10.052 (sec). Leaf size: 666
ode=( y[x]+2*x^3 )+( 2*x-x^4/y[x] )*D[y[x],{x,1}]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,5\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,6\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^7 x+16807 \text {$\#$1}^5 e^{7 c_1}-12005 \text {$\#$1}^4 e^{7 c_1} x^3+3430 \text {$\#$1}^3 e^{7 c_1} x^6-490 \text {$\#$1}^2 e^{7 c_1} x^9+35 \text {$\#$1} e^{7 c_1} x^{12}-e^{7 c_1} x^{15}\&,7\right ] \end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*x**3 + (-x**4/y(x) + 2*x)*Derivative(y(x), x) + y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE Derivative(y(x), x) - (2*x**3 + y(x))*y(x)/(x*(x**3 - 2*y(x))) c