Internal problem ID [4136]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 900.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {x^{2} {y^{\prime }}^{2}-\left (1+2 y x \right ) y^{\prime }+y^{2}=-1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 42
dsolve(x^2*diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+1+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {4 x^{2}-1}{4 x} y \left (x \right ) = c_{1} x -\sqrt {c_{1} -1} y \left (x \right ) = c_{1} x +\sqrt {c_{1} -1} \end{align*}
✓ Solution by Mathematica
Time used: 1.522 (sec). Leaf size: 66
DSolve[x^2 (y'[x])^2-(1+2 x y[x])y'[x]+1+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^{-2 c_1} x+e^{-c_1} y(x)\to x+\frac {1}{4} e^{-2 c_1} x+\frac {e^{-c_1}}{2} y(x)\to x y(x)\to x-\frac {1}{4 x} \end{align*}