Internal problem ID [13471]
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: 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {x \left (1-2 y\right )+\left (-x^{2}+y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(x*(1-2*y(x))+(y(x)-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x^{2}-\sqrt {x^{4}-x^{2}-2 c_{1}} \\ y \left (x \right ) &= x^{2}+\sqrt {x^{4}-x^{2}-2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 66
DSolve[x*(1-2*y[x])+(y[x]-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-i \sqrt {-x^4+x^2-c_1} \\ y(x)\to x^2+i \sqrt {-x^4+x^2-c_1} \\ y(x)\to \frac {1}{2} \\ \end{align*}