Internal problem ID [13407]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]
\[ \boxed {2 y^{3} x +3 y^{\prime } y^{2} x^{2}=-4 x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 73
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 \left (x \right ) &= \frac {{\left (x \left (-x^{4}+c_{1} \right )\right )}^{\frac {1}{3}}}{x} \\ y \left (x \right ) &= -\frac {{\left (x \left (-x^{4}+c_{1} \right )\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2 x} \\ y \left (x \right ) &= \frac {{\left (x \left (-x^{4}+c_{1} \right )\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 78
DSolve[2*x*y[x]^3+4*x^3+3*x^2*y[x]^2*y'[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*}