84.16.12 problem 8.21

Internal problem ID [22192]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.21
Date solved : Thursday, October 02, 2025 at 08:33:53 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 18

ode:=diff(y(x),x)+2*y(x)/x = -x^9*y(x)^5; 
ic:=[y(-1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2}{\left (32 x^{2}-31\right )^{{1}/{4}} x^{2}} \]

✓ Mathematica. Time used: 0.711 (sec). Leaf size: 22

ode=D[y[x],x]+2/x*y[x]==-x^9*y[x]^5; 
ic={y[-1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{\sqrt [4]{x^8 \left (32 x^2-31\right )}} \end{align*}

✓ Sympy. Time used: 2.780 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**9*y(x)**5 + Derivative(y(x), x) + 2*y(x)/x,0) 
ics = {y(-1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [4]{\frac {1}{x^{8} \left (2 x^{2} - \frac {31}{16}\right )}} \]