2.387   ODE No. 387

\[ y'(x)^2+e^x \left (y'(x)-y(x)\right )=0 \]

✓ Mathematica : cpu = 1.67852 (sec), leaf count = 136

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

\[\left \{\text {Solve}\left [\log (y(x))-\frac {-e^{x/2} \sqrt {4 y(x)+e^x}-4 y(x) \tanh ^{-1}\left (\frac {e^{x/2}}{\sqrt {4 y(x)+e^x}}\right )+e^x}{2 y(x)}=c_1,y(x)\right ],\text {Solve}\left [\log (y(x))-\frac {e^{x/2} \sqrt {4 y(x)+e^x}+4 y(x) \tanh ^{-1}\left (\frac {e^{x/2}}{\sqrt {4 y(x)+e^x}}\right )+e^x}{2 y(x)}=c_1,y(x)\right ]\right \}\]

✓ Maple : cpu = 0.724 (sec), leaf count = 118

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

\[2 \ln \left (y \left (x \right )\right )+\frac {\sqrt {{\mathrm e}^{2 x}+4 y \left (x \right ) {\mathrm e}^{x}}}{y \left (x \right )}+4 \,\operatorname {arctanh}\left (\sqrt {{\mathrm e}^{2 x}+4 y \left (x \right ) {\mathrm e}^{x}}\, {\mathrm e}^{-x}\right )-\frac {{\mathrm e}^{x}}{y \left (x \right )}-c_{1} = 0\]