Internal problem ID [6029]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 16.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x +y\right )^{2} \left (y^{\prime }\right )^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (-x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.057 (sec). Leaf size: 85
dsolve((y(x)+x)^2*diff(y(x),x)^2+(2*y(x)^2+x*y(x)-x^2)*diff(y(x),x)+y(x)*(y(x)-x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x -\sqrt {x^{2}+2 c_{1}} \\ y \relax (x ) = -x +\sqrt {x^{2}+2 c_{1}} \\ y \relax (x ) = \frac {-c_{1} x -\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y \relax (x ) = \frac {-c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.324 (sec). Leaf size: 164
DSolve[(y[x]+x)^2*(y'[x])^2+(2*y[x]^2+x*y[x]-x^2)*y'[x]+y[x]*(y[x]-x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {x^2+c_1{}^2} \\ y(x)\to -x+\sqrt {x^2+c_1{}^2} \\ y(x)\to -x-\sqrt {2 x^2+c_1{}^2} \\ y(x)\to -x+\sqrt {2 x^2+c_1{}^2} \\ y(x)\to -\sqrt {x^2}-x \\ y(x)\to \sqrt {x^2}-x \\ y(x)\to -\sqrt {2} \sqrt {x^2}-x \\ y(x)\to \sqrt {2} \sqrt {x^2}-x \\ \end{align*}