Internal problem ID [13409]
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 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, _Bernoulli]
\[ \boxed {3 x^{2} y^{2}+\left (2 y x^{3}+6 y\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(1+3*x^2*y(x)^2+(2*x^3*y(x)+6*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (x^{3}+3\right ) \left (c_{1} -x \right )}}{x^{3}+3} \\ y \left (x \right ) &= -\frac {\sqrt {\left (x^{3}+3\right ) \left (c_{1} -x \right )}}{x^{3}+3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 50
DSolve[1+3*x^2*y[x]^2+(2*x^3*y[x]+6*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x+c_1}}{\sqrt {x^3+3}} \\ y(x)\to \frac {\sqrt {-x+c_1}}{\sqrt {x^3+3}} \\ \end{align*}