2.474   ODE No. 474

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

\[ 2 y(x) y'(x)^2-(4 x-5) y'(x)+2 y(x)=0 \] Mathematica : cpu = 0.193005 (sec), leaf count = 135

\[\left \{\left \{y(x)\to -i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}}\right \},\left \{y(x)\to i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}}\right \},\left \{y(x)\to -\frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}}\right \},\left \{y(x)\to \frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}}\right \}\right \}\] Maple : cpu = 0.999 (sec), leaf count = 152

\[\left \{-c_{1}-\arctanh \left (\frac {1}{\sqrt {-\frac {16 y \left (x \right )^{2}}{\left (4 x -5\right )^{2}}+1}}\right )+\ln \left (\frac {y \left (x \right )}{4 x -5}\right )+\ln \left (x -\frac {5}{4}\right )-\frac {\ln \left (\frac {4 y \left (x \right )}{4 x -5}-1\right )}{2}-\frac {\ln \left (\frac {4 y \left (x \right )}{4 x -5}+1\right )}{2}+\frac {\ln \left (\frac {16 y \left (x \right )^{2}}{\left (4 x -5\right )^{2}}-1\right )}{2}-\frac {\sqrt {4}\, \sqrt {\frac {-16 y \left (x \right )^{2}+16 \left (x -\frac {5}{4}\right )^{2}}{\left (4 x -5\right )^{2}}}}{2}+\sqrt {-\frac {16 y \left (x \right )^{2}}{\left (4 x -5\right )^{2}}+1} = 0, y \left (x \right ) = -x +\frac {5}{4}, y \left (x \right ) = x -\frac {5}{4}\right \}\]