2.98   ODE No. 98

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

\[ a y(x)^2+c x^{2 b}-b y(x)+x y'(x)=0 \] Mathematica : cpu = 0.0250049 (sec), leaf count = 123

\[\left \{\left \{y(x)\to \frac {\sqrt {-c} x^b \left (c_1 \sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )-\cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )\right )}{\sqrt {-a} \left (\sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )+c_1 \cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )\right )}\right \}\right \}\]

Maple : cpu = 0.046 (sec), leaf count = 38

\[ \left \{ y \left ( x \right ) =-{\frac {1}{{x}^{-b}}\tan \left ( {\frac {1}{b} \left ( {x}^{b}\sqrt {c}\sqrt {a}+{\it \_C1}\,b \right ) } \right ) \sqrt {c}{\frac {1}{\sqrt {a}}}} \right \} \]