73.6.17 problem 7.5 (g)

Internal problem ID [15156]
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 (g)
Date solved : Tuesday, January 28, 2025 at 07:38:34 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(2*y(x)^3+(4*x^3*y(x)^3-3*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \frac {\operatorname {RootOf}\left (\textit {\_Z}^{32} c_{1} -\textit {\_Z}^{24} c_{1} -x^{8}\right )^{8}}{x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.354 (sec). Leaf size: 88

DSolve[2*y[x]^3+(4*x^3*y[x]^3-3*x*y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ \text {Solve}\left [\int _1^{\frac {(-1)^{2/3} \left (8 x^2 y(x)-15\right )}{\sqrt [3]{70} \left (4 x^2 y(x)-3\right )}}\frac {1}{K[1]^3+\frac {39 \sqrt [3]{-1} K[1]}{70^{2/3}}+1}dK[1]&=\frac {2}{27} (-70)^{2/3} \log (x)+c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}