50.3.17 problem 3(a)

Internal problem ID [7841]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 3(a)
Date solved : Wednesday, March 05, 2025 at 05:07:32 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=x^{4} y^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 34

ode:=x*diff(y(x),x)+y(x) = x^4*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {-x^{2}+c_{1}}\, x} \\ y &= -\frac {1}{\sqrt {-x^{2}+c_{1}}\, x} \\ \end{align*}

✓ Mathematica. Time used: 0.495 (sec). Leaf size: 48

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

\begin{align*} y(x)\to -\frac {1}{\sqrt {-x^4+c_1 x^2}} \\ y(x)\to \frac {1}{\sqrt {-x^4+c_1 x^2}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.705 (sec). Leaf size: 29

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

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