2.389   ODE No. 389

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

\[ y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0 \] Mathematica : cpu = 0.0806726 (sec), leaf count = 57

\[\left \{\left \{y(x)\to -\frac {1}{4} e^{x-4 c_1} \left (-e^x+2 e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{4} e^{x+2 c_1} \left (-2+e^{x+2 c_1}\right )\right \}\right \}\] Maple : cpu = 0.529 (sec), leaf count = 71

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