Internal problem ID [13421]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.5 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.922 (sec). Leaf size: 29
dsolve(4*x*y(x)+(3*x^2+5*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (x^{5} \textit {\_Z}^{25}+x^{5} \textit {\_Z}^{15}-c_{1} \right )^{10} x^{2} \]
✓ Solution by Mathematica
Time used: 60.064 (sec). Leaf size: 1121
DSolve[4*x*y[x]+(3*x^2+5*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,1\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,2\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,3\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,4\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,5\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,6\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,7\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,8\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,9\right ]} \\ y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,10\right ]} \\ \end{align*}