#### 2.387   ODE No. 387

$y'(x)^2+e^x \left (y'(x)-y(x)\right )=0$ Mathematica : cpu = 1.18554 (sec), leaf count = 190

$\left \{\text {Solve}\left [\log (y(x))-\frac {-e^{x/2} \sqrt {4 y(x)+e^x}-\frac {4 \sqrt {\frac {e^x}{y(x)}+4} y(x)^{3/2} \sinh ^{-1}\left (\frac {e^{x/2}}{2 \sqrt {y(x)}}\right )}{\sqrt {4 y(x)+e^x}}+e^x}{2 y(x)}=c_1,y(x)\right ],\text {Solve}\left [\log (y(x))-\frac {e^{x/2} \sqrt {4 y(x)+e^x}+\frac {4 \sqrt {\frac {e^x}{y(x)}+4} y(x)^{3/2} \sinh ^{-1}\left (\frac {e^{x/2}}{2 \sqrt {y(x)}}\right )}{\sqrt {4 y(x)+e^x}}+e^x}{2 y(x)}=c_1,y(x)\right ]\right \}$ Maple : cpu = 1.402 (sec), leaf count = 115

$\left \{ \ln \left ( y \left ( x \right ) \right ) -{\frac {1}{2\,y \left ( x \right ) }\sqrt {{{\rm e}^{2\,x}}+4\,y \left ( x \right ) {{\rm e}^{x}}}}-2\,{\it Artanh} \left ( \sqrt {{{\rm e}^{2\,x}}+4\,y \left ( x \right ) {{\rm e}^{x}}}{{\rm e}^{-x}} \right ) -{\frac {{{\rm e}^{x}}}{2\,y \left ( x \right ) }}-{\it \_C1}=0,\ln \left ( y \left ( x \right ) \right ) +{\frac {1}{2\,y \left ( x \right ) }\sqrt {{{\rm e}^{2\,x}}+4\,y \left ( x \right ) {{\rm e}^{x}}}}+2\,{\it Artanh} \left ( \sqrt {{{\rm e}^{2\,x}}+4\,y \left ( x \right ) {{\rm e}^{x}}}{{\rm e}^{-x}} \right ) -{\frac {{{\rm e}^{x}}}{2\,y \left ( x \right ) }}-{\it \_C1}=0 \right \}$