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 : Monday, January 27, 2025 at 03:24:30 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

dsolve(x*diff(y(x),x)+y(x)=x^4*y(x)^3,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*}

✓ Solution by Mathematica

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

DSolve[x*D[y[x],x]+y[x]==x^4*y[x]^3,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*}