15.8.44 problem 46

Internal problem ID [3047]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 46
Date solved : Sunday, March 30, 2025 at 01:13:54 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=x^{3} y^{6} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.603 (sec). Leaf size: 53

ode:=x*diff(y(x),x)+y(x) = x^3*y(x)^6; 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (-\sqrt {5}-1+i \sqrt {10-2 \sqrt {5}}\right ) 2^{{1}/{5}} \left (-x^{2} \left (3 x^{2}-5\right )^{4}\right )^{{1}/{5}}}{12 x^{3}-20 x} \]

✓ Mathematica. Time used: 1.062 (sec). Leaf size: 26

ode=x*D[y[x],x]+y[x]==x^3*y[x]^6; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sqrt [5]{2}}{\sqrt [5]{5 x^3-3 x^5}} \]

✓ Sympy. Time used: 13.279 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*y(x)**6 + x*Derivative(y(x), x) + y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [5]{2} \sqrt [5]{\frac {1}{x^{3} \left (5 - 3 x^{2}\right )}} \]