9.8.41 problem 43

Internal problem ID [3044]
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 : 43
Date solved : Tuesday, September 30, 2025 at 06:24:34 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }-2 y-2 x^{4} y^{3}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 18

ode:=x*diff(y(x),x)-2*y(x)-2*x^4*y(x)^3 = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 x^{2}}{\sqrt {-2 x^{8}+6}} \]

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 25

ode=x*D[y[x],x]+(-2*y[x]-2*x^4*y[x]^3)==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\sqrt {2} x^2}{\sqrt {3-x^8}} \end{align*}

✓ Sympy. Time used: 0.577 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**4*y(x)**3 + x*Derivative(y(x), x) - 2*y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {2} x^{2} \sqrt {\frac {1}{3 - x^{8}}} \]