#### 2.376   ODE No. 376

$a y'(x)+b y(x)+y'(x)^2=0$ Mathematica : cpu = 0.229626 (sec), leaf count = 110

$\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {\#1} b}+a \log \left (a-\sqrt {a^2-4 \text {\#1} b}\right )}{2 b}\& \right ]\left [c_1+\frac {x}{2}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {\#1} b}-a \log \left (\sqrt {a^2-4 \text {\#1} b}+a\right )}{2 b}\& \right ]\left [c_1-\frac {x}{2}\right ]\right \}\right \}$ Maple : cpu = 0.524 (sec), leaf count = 219

$\left \{ y \left ( x \right ) =-{\frac {1}{4\,b}{{\rm e}^{{\frac {1}{2\,a} \left ( -2\,a{\it lambertW} \left ( 2\,{\frac {{{\rm e}^{-1}}}{a}{{\rm e}^{{\frac {{\it \_C1}\,b}{a}}}}{\frac {1}{\sqrt {-{b}^{-1}}}} \left ( {{\rm e}^{{\frac {bx}{a}}}} \right ) ^{-1}} \right ) -a\ln \left ( -{\frac {1}{4\,b}} \right ) -2\,a+ \left ( -2\,x+2\,{\it \_C1} \right ) b \right ) }}} \left ( {{\rm e}^{{\frac {1}{2\,a} \left ( -2\,a{\it lambertW} \left ( 2\,{\frac {{{\rm e}^{-1}}}{a}{{\rm e}^{{\frac {{\it \_C1}\,b}{a}}}}{\frac {1}{\sqrt {-{b}^{-1}}}} \left ( {{\rm e}^{{\frac {bx}{a}}}} \right ) ^{-1}} \right ) -a\ln \left ( -{\frac {1}{4\,b}} \right ) -2\,a+ \left ( -2\,x+2\,{\it \_C1} \right ) b \right ) }}}+2\,a \right ) },y \left ( x \right ) =-{\frac {1}{4\,b}{{\rm e}^{{\it RootOf} \left ( -a\ln \left ( -{\frac { \left ( {{\rm e}^{{\it \_Z}}}+2\,a \right ) ^{2}}{4\,b}} \right ) +2\,{\it \_C1}\,b-2\,bx+2\,{{\rm e}^{{\it \_Z}}}+2\,a \right ) }} \left ( {{\rm e}^{{\it RootOf} \left ( -a\ln \left ( -{\frac { \left ( {{\rm e}^{{\it \_Z}}}+2\,a \right ) ^{2}}{4\,b}} \right ) +2\,{\it \_C1}\,b-2\,bx+2\,{{\rm e}^{{\it \_Z}}}+2\,a \right ) }}+2\,a \right ) } \right \}$