31.3.4 problem 5.2

Internal problem ID [5734]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 4
Problem number : 5.2
Date solved : Monday, January 27, 2025 at 01:11:59 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.198 (sec). Leaf size: 38

dsolve((8*y(x)+10*x)+(5*y(x)+7*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (\operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} x^{5}-2 \textit {\_Z}^{20} c_{1} x^{5}+\textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5}-2\right ) \]

✓ Solution by Mathematica

Time used: 2.285 (sec). Leaf size: 276

DSolve[(8*y[x]+10*x)+(5*y[x]+7*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,5\right ] \\ \end{align*}