40.3.32 problem 26 (f)

Internal problem ID [6636]
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)
Date solved : Monday, January 27, 2025 at 02:16:27 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.706 (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)
 

\[ y = \frac {\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{12}+4 c_1 \,\textit {\_Z}^{3}-x^{3}\right )^{9}+4}{x^{3}} \]

✓ Solution by Mathematica

Time used: 60.292 (sec). Leaf size: 1175

DSolve[(3*x^2*y[x]^2)+4*(x^3*y[x]-3)*D[y[x],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*}