26.3.6 problem 4(c)

Internal problem ID [4266]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(c)
Date solved : Sunday, March 30, 2025 at 02:48:06 AM
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: 0.219 (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: 0.344 (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)
 

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