70.1.22 problem 22

Internal problem ID [18608]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 22
Date solved : Thursday, October 02, 2025 at 03:16:03 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2^{{1}/{3}} \\ \end{align*}

✓ Maple. Time used: 0.336 (sec). Leaf size: 27

ode:=diff(y(x),x) = 1/6*x*(x^2+1)*y(x)^5; 
ic:=[y(0) = -2^(1/3)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\sqrt {6}}{\left (-6 x^{4}+9 \,2^{{2}/{3}}-12 x^{2}\right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 36

ode=D[y[x],x]==x*(x^2+1)/6*y[x]^5; 
ic={y[0]==-2^(1/3)}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {2}}{\sqrt [4]{-\frac {2 x^4}{3}-\frac {4 x^2}{3}+2^{2/3}}} \end{align*}

✓ Sympy. Time used: 0.877 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(x**2 + 1)*y(x)**5/6 + Derivative(y(x), x),0) 
ics = {y(0): -2**(1/3)} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \sqrt [4]{6} \sqrt [4]{- \frac {1}{x^{4} + 2 x^{2} - \frac {3 \cdot 2^{\frac {2}{3}}}{2}}} \]