78.5.22 problem 4 (k)

Internal problem ID [18165]
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 9 (Integrating Factors). Problems at page 80
Problem number : 4 (k)
Date solved : Tuesday, January 28, 2025 at 11:35:49 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x y^{\prime }+y+x^{2} y^{5} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 29

dsolve(x*diff(y(x),x)+y(x)+ x^2*y(x)^5*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {c_1 \operatorname {RootOf}\left (c_1^{5} \textit {\_Z}^{5}-x^{4} \textit {\_Z} -4 x^{4}\right )}{x} \]

✓ Solution by Mathematica

Time used: 1.786 (sec). Leaf size: 116

DSolve[x*D[y[x],x]+y[x]+x^2*y[x]^5*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5 x-4 \text {$\#$1} c_1 x-4\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5 x-4 \text {$\#$1} c_1 x-4\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5 x-4 \text {$\#$1} c_1 x-4\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5 x-4 \text {$\#$1} c_1 x-4\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5 x-4 \text {$\#$1} c_1 x-4\&,5\right ] \\ y(x)\to 0 \\ \end{align*}