Internal problem ID [12119]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (x +y\right ) y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve((y(x)-x)+(y(x)+x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-c_{1} x -\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} y \left (x \right ) = \frac {-c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.763 (sec). Leaf size: 94
DSolve[(y[x]-x)+(y[x]+x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {2 x^2+e^{2 c_1}} y(x)\to -x+\sqrt {2 x^2+e^{2 c_1}} y(x)\to -\sqrt {2} \sqrt {x^2}-x y(x)\to \sqrt {2} \sqrt {x^2}-x \end{align*}