66.1.2 problem Problem 2

Internal problem ID [13849]
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
Date solved : Tuesday, January 28, 2025 at 06:05:06 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 2.104 (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)
 

\[ y = -\operatorname {RootOf}\left (128 \textit {\_Z}^{25} c_{1} x^{5}+640 \textit {\_Z}^{20} c_{1} x^{5}+800 \textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5} x -4 x +\frac {3}{2} \]

✓ Solution by Mathematica

Time used: 60.061 (sec). Leaf size: 1121

DSolve[(12*x+6*y[x]-9)+(5*x+2*y[x]-3)*D[y[x],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*}