Internal problem ID [5420]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }+y-x^{4} y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(x*diff(y(x),x)+y(x)=x^4*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {-x^{2}+c_{1}}\, x} \\ y \relax (x ) = -\frac {1}{\sqrt {-x^{2}+c_{1}}\, x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.562 (sec). Leaf size: 48
DSolve[x*y'[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*}