Internal problem ID [4029]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 789.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-2 x y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 65
dsolve(diff(y(x),x)^2-2*x*diff(y(x),x)+1 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2}-\frac {\sqrt {x^{2}-1}\, x}{2}+\frac {\ln \left (x +\sqrt {x^{2}-1}\right )}{2}+c_{1} \\ y \left (x \right ) &= \frac {x^{2}}{2}+\frac {\sqrt {x^{2}-1}\, x}{2}-\frac {\ln \left (x +\sqrt {x^{2}-1}\right )}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 90
DSolve[(y'[x])^2-2 x y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-2 \text {arctanh}\left (\frac {\sqrt {x^2-1}}{x-1}\right )+x^2+\sqrt {x^2-1} x+2 c_1\right ) \\ y(x)\to \text {arctanh}\left (\frac {\sqrt {x^2-1}}{x-1}\right )+\frac {x^2}{2}-\frac {1}{2} \sqrt {x^2-1} x+c_1 \\ \end{align*}