Internal problem ID [1071]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {12 y x^{3}+24 x^{2} y^{2}+\left (9 x^{4}+32 y x^{3}+4 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 27
dsolve((12*x^3*y(x)+24*x^2*y(x)^2)+(9*x^4+32*x^3*y(x)+4*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ 3 x^{4} y \relax (x )^{3}+8 x^{3} y \relax (x )^{4}+y \relax (x )^{4}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.533 (sec). Leaf size: 1733
DSolve[(12*x^3*y[x]+24*x^2*y[x]^2)+(9*x^4+32*x^3*y[x]+4*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 x^4}{32 x^3+4}+\frac {1}{2} \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}-\frac {1}{2} \sqrt {\frac {9 x^8}{2 \left (8 x^3+1\right )^2}-\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}+\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}-\frac {27 x^{12}}{4 \left (8 x^3+1\right )^3 \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}}} \\ y(x)\to -\frac {3 x^4}{32 x^3+4}+\frac {1}{2} \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}+\frac {1}{2} \sqrt {\frac {9 x^8}{2 \left (8 x^3+1\right )^2}-\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}+\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}-\frac {27 x^{12}}{4 \left (8 x^3+1\right )^3 \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}}} \\ y(x)\to -\frac {3 x^4}{32 x^3+4}-\frac {1}{2} \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}-\frac {1}{2} \sqrt {\frac {9 x^8}{2 \left (8 x^3+1\right )^2}-\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}+\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}+\frac {27 x^{12}}{4 \left (8 x^3+1\right )^3 \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}}} \\ y(x)\to -\frac {3 x^4}{32 x^3+4}-\frac {1}{2} \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}+\frac {1}{2} \sqrt {\frac {9 x^8}{2 \left (8 x^3+1\right )^2}-\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}+\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}+\frac {27 x^{12}}{4 \left (8 x^3+1\right )^3 \sqrt {\frac {9 x^8}{4 \left (8 x^3+1\right )^2}+\frac {\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}{3 \sqrt [3]{2} \left (8 x^3+1\right )}-\frac {4 \sqrt [3]{2} c_1}{\sqrt [3]{\sqrt {59049 c_1{}^2 x^{16}+6912 c_1{}^3 \left (8 x^3+1\right )^3}-243 c_1 x^8}}}}} \\ \end{align*}