Internal problem ID [12150]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 72.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (x -2 y\right ) y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve((x^2+y(x))+(x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {x}{2}-\frac {\sqrt {12 x^{3}+9 x^{2}+36 c_{1}}}{6} y \left (x \right ) = \frac {x}{2}+\frac {\sqrt {12 x^{3}+9 x^{2}+36 c_{1}}}{6} \end{align*}
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 81
DSolve[(x^2+y[x])+(x-2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (3 x-i \sqrt {3} \sqrt {-4 x^3-3 x^2-12 c_1}\right ) y(x)\to \frac {1}{6} \left (3 x+i \sqrt {3} \sqrt {-4 x^3-3 x^2-12 c_1}\right ) \end{align*}