Internal problem ID [3967]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Example
10.83, page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {y \left (2 y^{3} x^{2}+3\right )+x \left (y^{3} x^{2}-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 39
dsolve((y(x)*(2*x^2*y(x)^3+3))+(x*(x^2*y(x)^3-1))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {11 c_{1}}{3}} x^{3}}{\RootOf \left (11 \,{\mathrm e}^{11 c_{1}} \textit {\_Z}^{15}-{\mathrm e}^{11 c_{1}} \textit {\_Z}^{11}+4 x^{11}\right )^{5}} \]
✓ Solution by Mathematica
Time used: 10.333 (sec). Leaf size: 1081
DSolve[(y[x]*(2*x^2*y[x]^3+3))+(x*(x^2*y[x]^3-1))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,1\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,2\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,3\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,4\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,5\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,6\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,7\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,8\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,9\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,10\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,11\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,12\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,13\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,14\right ] \\ y(x)\to \text {Root}\left [1024 \text {$\#$1}^{15} x^{22}+14080 \text {$\#$1}^{12} x^{20}+77440 \text {$\#$1}^9 x^{18}+212960 \text {$\#$1}^6 x^{16}-\text {$\#$1}^4 e^{\frac {44 c_1}{3}}+292820 \text {$\#$1}^3 x^{14}+161051 x^{12}\&,15\right ] \\ \end{align*}