Internal problem ID [12113]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {6 y+\left (5 x +2 y-3\right ) y^{\prime }=-12 x +9} \]
✓ Solution by Maple
Time used: 0.89 (sec). Leaf size: 44
dsolve((12*x+6*y(x)-9)+(5*x+2*y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {RootOf}\left (128 \textit {\_Z}^{25} c_{1} x^{5}+640 \textit {\_Z}^{20} c_{1} x^{5}+800 \textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5} x -4 x +\frac {3}{2} \]
✓ Solution by Mathematica
Time used: 60.12 (sec). Leaf size: 1121
DSolve[(12*x+6*y[x]-9)+(5*x+2*y[x]-3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,1\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,2\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,3\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,4\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,5\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,6\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,7\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,8\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,9\right ]} \\ y(x)\to \frac {1}{2} (3-5 x)+\frac {1}{2 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{10}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^8-1080 \text {$\#$1}^7 x^7+3105 \text {$\#$1}^6 x^6+666 \text {$\#$1}^5 x^5-425 \text {$\#$1}^4 x^4-140 \text {$\#$1}^3 x^3+15 \text {$\#$1}^2 x^2+10 \text {$\#$1} x+1\&,10\right ]} \\ \end{align*}