Internal problem ID [5293]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 26 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {3 y^{2} x^{2}+4 \left (y x^{3}-3\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 1.297 (sec). Leaf size: 30
dsolve((3*x^2*y(x)^2)+4*(x^3*y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{12} c_{1} +4 \textit {\_Z}^{3} c_{1} -x^{3}\right )^{9}+4}{x^{3}} \]
✓ Solution by Mathematica
Time used: 60.296 (sec). Leaf size: 1175
DSolve[(3*x^2*y[x]^2)+4*(x^3*y[x]-3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^3}-\frac {\sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}{\sqrt {6}}-\frac {1}{2} \sqrt {\frac {2 c_1}{\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}+\frac {8}{x^6}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}{3^{2/3} x^3}-\frac {8 \sqrt {6}}{x^9 \sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}} \\ y(x)\to \frac {1}{x^3}-\frac {\sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}{\sqrt {6}}+\frac {1}{2} \sqrt {\frac {2 c_1}{\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}+\frac {8}{x^6}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}{3^{2/3} x^3}-\frac {8 \sqrt {6}}{x^9 \sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}} \\ y(x)\to \frac {1}{x^3}+\frac {\sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}{\sqrt {6}}-\frac {1}{2} \sqrt {\frac {2 c_1}{\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}+\frac {8}{x^6}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}{3^{2/3} x^3}+\frac {8 \sqrt {6}}{x^9 \sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}} \\ y(x)\to \frac {1}{x^3}+\frac {\sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}{\sqrt {6}}+\frac {1}{2} \sqrt {\frac {2 c_1}{\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}+\frac {8}{x^6}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}{3^{2/3} x^3}+\frac {8 \sqrt {6}}{x^9 \sqrt {-\frac {3^{2/3} c_1}{\sqrt [3]{\sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-9 c_1}}+\frac {6}{x^6}+\frac {\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^2 \left (27+c_1 x^9\right )}-27 c_1}}{x^3}}}} \\ \end{align*}