73.6.4 problem 7.4 (b)

Internal problem ID [15143]
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 : 7.4 (b)
Date solved : Tuesday, January 28, 2025 at 07:36:42 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 71

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

\begin{align*} y &= \frac {{\left (x \left (-x^{4}+c_{1} \right )\right )}^{{1}/{3}}}{x} \\ y &= -\frac {{\left (x \left (-x^{4}+c_{1} \right )\right )}^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2 x} \\ y &= \frac {{\left (x \left (-x^{4}+c_{1} \right )\right )}^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 78

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

\begin{align*} y(x)\to \frac {\sqrt [3]{-x^4+c_1}}{x^{2/3}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^4+c_1}}{x^{2/3}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^4+c_1}}{x^{2/3}} \\ \end{align*}