Internal problem ID [4221]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 989.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-\left (-y+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 85
dsolve((x+y(x))^2*diff(y(x),x)^2-(x^2-x*y(x)-2*y(x)^2)*diff(y(x),x)-(x-y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x -\sqrt {x^{2}+2 c_{1}} y \left (x \right ) = -x +\sqrt {x^{2}+2 c_{1}} 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: 0.592 (sec). Leaf size: 172
DSolve[(x+y[x])^2 (y'[x])^2 -(x^2-x y[x]-2 y[x]^2) y'[x]-(x-y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {x^2+e^{2 c_1}} y(x)\to -x+\sqrt {x^2+e^{2 c_1}} 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 {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*}