2.374   ODE No. 374

\[ y'(x)^2-2 y'(x)-y(x)^2=0 \]

✓ Mathematica : cpu = 0.409663 (sec), leaf count = 99

DSolve[-y[x]^2 - 2*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}+\text {$\#$1} \log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )+1}{\text {$\#$1}}\& \right ][-x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )+\frac {1}{\text {$\#$1}}\& \right ][x+c_1]\right \}\right \}\]

✓ Maple : cpu = 0.028 (sec), leaf count = 85

dsolve(diff(y(x),x)^2-2*diff(y(x),x)-y(x)^2 = 0,y(x))
 

\[x -\frac {1}{y \left (x \right )}-\frac {\left (y \left (x \right )^{2}+1\right )^{{3}/{2}}}{y \left (x \right )}+y \left (x \right ) \sqrt {y \left (x \right )^{2}+1}+\operatorname {arcsinh}\left (y \left (x \right )\right )-c_{1} = 0\]