78.5.25 problem 5
Internal
problem
ID
[18089]
Book
:
DIFFERENTIAL
EQUATIONS
WITH
APPLICATIONS
AND
HISTORICAL
NOTES
by
George
F.
Simmons.
3rd
edition.
2017.
CRC
press,
Boca
Raton
FL.
Section
:
Chapter
2.
First
order
equations.
Section
9
(Integrating
Factors).
Problems
at
page
80
Problem
number
:
5
Date
solved
:
Thursday, March 13, 2025 at 11:35:40 AM
CAS
classification
:
[[_homogeneous, `class G`]]
\begin{align*} y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \end{align*}
✓ Maple. Time used: 0.500 (sec). Leaf size: 176
ode:=diff(y(x),x) = 2*y(x)/x+x^3/y(x)+x*tan(1/x^2*y(x));
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {x^{2} \left (-c_1 \cot \left (\operatorname {RootOf}\left (2 c_1^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_1^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_1 \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right )+x \csc \left (\operatorname {RootOf}\left (2 c_1^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_1^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_1 \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right )\right )}{c_1} \\
y &= \frac {x^{2} \left (c_1 \cot \left (\operatorname {RootOf}\left (2 c_1^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_1^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_1 \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right )+x \csc \left (\operatorname {RootOf}\left (2 c_1^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_1^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_1 \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right )\right )}{c_1} \\
\end{align*}
✓ Mathematica. Time used: 1.098 (sec). Leaf size: 36
ode=D[y[x],x]==2*y[x]/x+x^3/y[x]+x*Tan[y[x]/x^2];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [3 \log (x)-\log \left (y(x) \sin \left (\frac {y(x)}{x^2}\right )+x^2 \cos \left (\frac {y(x)}{x^2}\right )\right )=c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x**3/y(x) - x*tan(y(x)/x**2) + Derivative(y(x), x) - 2*y(x)/x,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out