15.5.2 problem 2
Internal
problem
ID
[2938]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
9,
page
38
Problem
number
:
2
Date
solved
:
Sunday, March 30, 2025 at 01:00:14 AM
CAS
classification
:
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} x y+\left (x^{2}+y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.220 (sec). Leaf size: 973
ode:=x*y(x)+(y(x)+x^2)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 60.04 (sec). Leaf size: 397
ode=x*y[x]+(x^2+y[x])*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -x^2+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,1\right ]} \\
y(x)\to -x^2+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,2\right ]} \\
y(x)\to -x^2+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,3\right ]} \\
y(x)\to -x^2+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,4\right ]} \\
y(x)\to -x^2+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,5\right ]} \\
y(x)\to -x^2+\frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,6\right ]} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*y(x) + (x**2 + y(x))*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out