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: 0.078 (sec). Leaf size: 66
dsolve(diff(y(x),x)^2-2*diff(y(x),x)-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} \frac {-\sqrt {y \left (x \right )^{2}+1}+\operatorname {arcsinh}\left (y \left (x \right )\right ) y \left (x \right )-1+\left (-c_{1} +x \right ) y \left (x \right )}{y \left (x \right )} &= 0 \\ \frac {\sqrt {y \left (x \right )^{2}+1}-\operatorname {arcsinh}\left (y \left (x \right )\right ) y \left (x \right )-1+\left (-c_{1} +x \right ) y \left (x \right )}{y \left (x \right )} &= 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*}