Internal problem ID [7954]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 374.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 y^{\prime }-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.217 (sec). Leaf size: 85
dsolve(diff(y(x),x)^2-2*diff(y(x),x)-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} x -\frac {1}{y \relax (x )}-\frac {\left (y \relax (x )^{2}+1\right )^{\frac {3}{2}}}{y \relax (x )}+y \relax (x ) \sqrt {y \relax (x )^{2}+1}+\arcsinh \left (y \relax (x )\right )-c_{1} = 0 \\ x +\frac {\left (y \relax (x )^{2}+1\right )^{\frac {3}{2}}}{y \relax (x )}-y \relax (x ) \sqrt {y \relax (x )^{2}+1}-\arcsinh \left (y \relax (x )\right )-\frac {1}{y \relax (x )}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.545 (sec). Leaf size: 100
DSolve[-y[x]^2 - 2*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}+\tanh ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\text {$\#$1}^2+1}}\right )-\frac {1}{\text {$\#$1}}\&\right ][-x+c_1] \\ y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}+\tanh ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\text {$\#$1}^2+1}}\right )+\frac {1}{\text {$\#$1}}\&\right ][x+c_1] \\ y(x)\to 0 \\ \end{align*}