78.5.14 problem 4 (c)

Internal problem ID [18086]
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 : 4 (c)
Date solved : Monday, March 31, 2025 at 05:07:36 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }&=x^{5}+x^{3} y^{2}+y \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

ode:=x*diff(y(x),x) = x^5+x^3*y(x)^2+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (\frac {x^{4}}{4}+c_1 \right ) x \]

✓ Mathematica. Time used: 0.194 (sec). Leaf size: 18

ode=x*D[y[x],x] == x^5+x^3*y[x]^2+y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \tan \left (\frac {x^4}{4}+c_1\right ) \]

✓ Sympy. Time used: 0.304 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 - x**3*y(x)**2 + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \left (i C_{1} e^{\frac {i x^{4}}{2}} + i e^{i x^{4}}\right )}{C_{1} e^{\frac {i x^{4}}{2}} - e^{i x^{4}}} \]