2.58   ODE No. 58

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

\[ a \left (-\sqrt {y(x)}\right )-b x+y'(x)=0 \] Mathematica : cpu = 0.218594 (sec), leaf count = 118

\[\text {Solve}\left [\frac {a^2 \left (-\log \left (a^2 \left (\sqrt {\frac {a^2 y(x)}{b^2 x^2}}+1\right )-\frac {2 a^2 y(x)}{b x^2}\right )-\frac {2 a \tanh ^{-1}\left (\frac {a \left (1-\frac {4 b \sqrt {\frac {a^2 y(x)}{b^2 x^2}}}{a^2}\right )}{\sqrt {a^2+8 b}}\right )}{\sqrt {a^2+8 b}}\right )}{2 b}=\frac {a^2 \log (x)}{b}+c_1,y(x)\right ]\] Maple : cpu = 0.065 (sec), leaf count = 68

\[ \left \{ -{\frac {1}{2}\ln \left ( \sqrt {y \left ( x \right ) }ax+b{x}^{2}-2\,y \left ( x \right ) \right ) }+{a\sqrt {y \left ( x \right ) }{\it Artanh} \left ( { \left ( a\sqrt {y \left ( x \right ) }+2\,bx \right ) {\frac {1}{\sqrt {y \left ( x \right ) \left ( {a}^{2}+8\,b \right ) }}}} \right ) {\frac {1}{\sqrt {y \left ( x \right ) \left ( {a}^{2}+8\,b \right ) }}}}+{\it \_C1}=0 \right \} \]