Internal problem ID [3628]
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]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.114 (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 \relax (x ) = \frac {4 x^{2}-1}{4 x} \\ y \relax (x ) = c_{1} x -\sqrt {c_{1}-1} \\ y \relax (x ) = c_{1} x +\sqrt {c_{1}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.715 (sec). Leaf size: 62
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} \left (x+e^{c_1}\right ) \\ y(x)\to x+\frac {1}{4} e^{-2 c_1} \left (x+2 e^{c_1}\right ) \\ y(x)\to x \\ y(x)\to x-\frac {1}{4 x} \\ \end{align*}