73.6.13 problem 7.5 (c)

Internal problem ID [15152]
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 (c)
Date solved : Tuesday, January 28, 2025 at 07:38:21 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 19.059 (sec). Leaf size: 28

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

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{32} c_{1} -\textit {\_Z}^{24} c_{1} -x^{8}\right )^{8}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.210 (sec). Leaf size: 77

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

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