Internal problem ID [4014]
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]
\[ \boxed {{y^{\prime }}^{2}-2 y^{\prime }-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.046 (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 \left (x \right )}-\frac {\left (1+y \left (x \right )^{2}\right )^{\frac {3}{2}}}{y \left (x \right )}+y \left (x \right ) \sqrt {1+y \left (x \right )^{2}}+\operatorname {arcsinh}\left (y \left (x \right )\right )-c_{1} = 0 x +\frac {\left (1+y \left (x \right )^{2}\right )^{\frac {3}{2}}}{y \left (x \right )}-y \left (x \right ) \sqrt {1+y \left (x \right )^{2}}-\operatorname {arcsinh}\left (y \left (x \right )\right )-\frac {1}{y \left (x \right )}-c_{1} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 1.359 (sec). Leaf size: 104
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 {$\#$1}^2+1}+\text {$\#$1} \log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )+1}{\text {$\#$1}}\&\right ][-x+c_1] y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )+\frac {1}{\text {$\#$1}}\&\right ][x+c_1] y(x)\to 0 \end{align*}