Internal problem ID [4365]
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`]]
\[ \boxed {8 y+\left (7 x +5 y\right ) y^{\prime }=-10 x} \]
✓ Solution by Maple
Time used: 0.437 (sec). Leaf size: 49
dsolve((8*y(x)+10*x)+(5*y(x)+7*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (-2 c_{1}^{2}+c_{1}^{2} \operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} x^{5}-2 \textit {\_Z}^{20} c_{1} x^{5}+\textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5}\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 2.163 (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*}