Internal problem ID [13434]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, _Bernoulli]
\[ \boxed {2 y^{2} x +\left (2 x^{2} y+2 y\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(1+2*x*y(x)^2+(2*x^2*y(x)+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (x^{2}+1\right ) \left (c_{1} -x \right )}}{x^{2}+1} \\ y \left (x \right ) &= -\frac {\sqrt {\left (x^{2}+1\right ) \left (c_{1} -x \right )}}{x^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 50
DSolve[1+2*x*y[x]^2+(2*x^2*y[x]+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x+c_1}}{\sqrt {x^2+1}} \\ y(x)\to \frac {\sqrt {-x+c_1}}{\sqrt {x^2+1}} \\ \end{align*}