2.376   ODE No. 376

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ a y'(x)+b y(x)+y'(x)^2=0 \] Mathematica : cpu = 0.262035 (sec), leaf count = 110

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {$\#$1} b}+a \log \left (a-\sqrt {a^2-4 \text {$\#$1} b}\right )}{2 b}\& \right ]\left [\frac {x}{2}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {$\#$1} b}-a \log \left (\sqrt {a^2-4 \text {$\#$1} b}+a\right )}{2 b}\& \right ]\left [-\frac {x}{2}+c_1\right ]\right \}\right \}\] Maple : cpu = 0.768 (sec), leaf count = 279

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