Internal problem ID [3506]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 774.
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: 0.09 (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 (1+y \relax (x )^{2}\right )^{\frac {3}{2}}}{y \relax (x )}+y \relax (x ) \sqrt {1+y \relax (x )^{2}}+\arcsinh \left (y \relax (x )\right )-c_{1} = 0 \\ x +\frac {\left (1+y \relax (x )^{2}\right )^{\frac {3}{2}}}{y \relax (x )}-y \relax (x ) \sqrt {1+y \relax (x )^{2}}-\arcsinh \left (y \relax (x )\right )-\frac {1}{y \relax (x )}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.523 (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*}