12.5.13 problem 9

Internal problem ID [1637]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 9
Date solved : Tuesday, March 04, 2025 at 12:58:07 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=x^{4} y^{4} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.069 (sec). Leaf size: 34

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

\[ y = \frac {\left (-\left (3 x -11\right )^{2}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{6 x^{2}-22 x} \]

✓ Mathematica. Time used: 0.613 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{\sqrt [3]{-x^3 (3 x-11)}} \]

✓ Sympy. Time used: 1.865 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \sqrt [3]{- \frac {1}{x^{3} \left (3 x - 11\right )}} \]