9.5.16 problem 20

Internal problem ID [2952]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 06:11:44 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y \left (1-x^{4} y^{2}\right )+x y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 18

ode:=y(x)*(1-x^4*y(x)^2)+x*diff(y(x),x) = 0; 
ic:=[y(1) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {1}{\sqrt {-x^{2}+2}\, x} \]

✓ Mathematica. Time used: 0.378 (sec). Leaf size: 21

ode=y[x]*(1-x^4*y[x]^2)+x*D[y[x],x]==0; 
ic={y[1]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{\sqrt {-x^2 \left (x^2-2\right )}} \end{align*}

✓ Sympy. Time used: 0.490 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (-x**4*y(x)**2 + 1)*y(x),0) 
ics = {y(1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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