2.403   ODE No. 403

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

\[ a y'(x)^2+b y'(x)-y(x)=0 \] Mathematica : cpu = 0.252719 (sec), leaf count = 116

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {4 \text {$\#$1} a+b^2}+b \log \left (b-\sqrt {4 \text {$\#$1} a+b^2}\right )}{2 a}\& \right ]\left [\frac {x}{2 a}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {4 \text {$\#$1} a+b^2}-b \log \left (\sqrt {4 \text {$\#$1} a+b^2}+b\right )}{2 a}\& \right ]\left [-\frac {x}{2 a}+c_1\right ]\right \}\right \}\] Maple : cpu = 0.815 (sec), leaf count = 247

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