2.403 ODE No. 403
\[ a y'(x)^2+b y'(x)-y(x)=0 \]
✓ Mathematica : cpu = 0.405654 (sec), leaf count = 118
DSolve[-y[x] + b*Derivative[1][y][x] + a*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {4 \text {$\#$1} a+b^2}+b \log \left (a \left (\sqrt {4 \text {$\#$1} a+b^2}-b\right )\right )}{2 a}\& \right ]\left [\frac {x}{2 a}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {4 \text {$\#$1} a+b^2}-b \log \left (\sqrt {4 \text {$\#$1} a+b^2}+b\right )}{2 a}\& \right ]\left [-\frac {x}{2 a}+c_1\right ]\right \}\right \}\]
✓ Maple : cpu = 0.886 (sec), leaf count = 247
dsolve(a*diff(y(x),x)^2+b*diff(y(x),x)-y(x) = 0,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{-\frac {b \ln \left (\frac {1}{4 a}\right )+2 b \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{-\frac {c_{1}}{b}} {\mathrm e}^{-1} {\mathrm e}^{\frac {x}{b}}}{b \sqrt {\frac {1}{a}}}\right )+2 c_{1} +2 b -2 x}{2 b}} \left ({\mathrm e}^{-\frac {b \ln \left (\frac {1}{4 a}\right )+2 b \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{-\frac {c_{1}}{b}} {\mathrm e}^{-1} {\mathrm e}^{\frac {x}{b}}}{b \sqrt {\frac {1}{a}}}\right )+2 c_{1} +2 b -2 x}{2 b}}+2 b \right )}{4 a}\]