2.41   ODE No. 41

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

\[ a x y(x)^3+b y(x)^2+y'(x)=0 \] Mathematica : cpu = 0.279243 (sec), leaf count = 103

\[\text {Solve}\left [-\frac {b^2 \left (\frac {2 \tan ^{-1}\left (\frac {-2 a x y(x)-b}{b \sqrt {-\frac {4 a}{b^2}-1}}\right )}{\sqrt {-\frac {4 a}{b^2}-1}}-\log \left (\frac {a (-x) y(x) (-a x y(x)-b)-a}{a^2 x^2 y(x)^2}\right )\right )}{2 a}=-\frac {b^2 \log (x)}{a}+c_1,y(x)\right ]\] Maple : cpu = 0.31 (sec), leaf count = 103

\[\left \{y \left (x \right ) = \frac {{\mathrm e}^{\RootOf \left (2 c_{1} b^{2}+2 \textit {\_Z} \,b^{2}-b^{2} \ln \left (\left (a \,{\mathrm e}^{2 \textit {\_Z}}+b \,{\mathrm e}^{\textit {\_Z}}-1\right ) x^{2}\right )+8 c_{1} a +8 \textit {\_Z} a -4 a \ln \left (\left (a \,{\mathrm e}^{2 \textit {\_Z}}+b \,{\mathrm e}^{\textit {\_Z}}-1\right ) x^{2}\right )+2 \sqrt {b^{2}+4 a}\, b \arctanh \left (\frac {2 a \,{\mathrm e}^{\textit {\_Z}}+b}{\sqrt {b^{2}+4 a}}\right )\right )}}{x}\right \}\]