Internal problem ID [3857]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 3.5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {8 y+10 x +\left (7 x +5 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.75 (sec). Leaf size: 51
dsolve((8*y(x)+10*x)+(5*y(x)+7*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (2 c_{1}^{2}-c_{1}^{2} \RootOf \left (\textit {\_Z}^{25} x^{5} c_{1}-2 \textit {\_Z}^{20} x^{5} c_{1}+\textit {\_Z}^{15} x^{5} c_{1}-1\right )^{5}\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 2.106 (sec). Leaf size: 276
DSolve[(8*y[x]+10*x)+(5*y[x]+7*x)*y'[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*}