2.376   ODE No. 376

\[ a y'(x)+b y(x)+y'(x)^2=0 \]

✓ Mathematica : cpu = 0.334609 (sec), leaf count = 114

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

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {$\#$1} b}+a \log \left (b \left (\sqrt {a^2-4 \text {$\#$1} b}-a\right )\right )}{2 b}\& \right ]\left [\frac {x}{2}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {$\#$1} b}-a \log \left (b \left (\sqrt {a^2-4 \text {$\#$1} b}+a\right )\right )}{2 b}\& \right ]\left [-\frac {x}{2}+c_1\right ]\right \}\right \}\]

✓ Maple : cpu = 0.895 (sec), leaf count = 279

dsolve(diff(y(x),x)^2+a*diff(y(x),x)+b*y(x) = 0,y(x))
 

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