78.6.11 problem 3 (a)

Internal problem ID [18179]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 3 (a)
Date solved : Tuesday, January 28, 2025 at 11:36:22 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.417 (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*}