2.477   ODE No. 477

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

\[ a y(x) y'(x)^2+(2 x-b) y'(x)-y(x)=0 \] Mathematica : cpu = 0.245232 (sec), leaf count = 146

\[\left \{\left \{y(x)\to -\frac {e^{\frac {c_1}{2}} \sqrt {2 b-4 x+e^{c_1}}}{2 \sqrt {a}}\right \},\left \{y(x)\to \frac {e^{\frac {c_1}{2}} \sqrt {2 b-4 x+e^{c_1}}}{2 \sqrt {a}}\right \},\left \{y(x)\to -\sqrt {2} e^{\frac {c_1}{2}} \sqrt {2 a e^{c_1}-b+2 x}\right \},\left \{y(x)\to \sqrt {2} e^{\frac {c_1}{2}} \sqrt {2 a e^{c_1}-b+2 x}\right \}\right \}\] Maple : cpu = 0.49 (sec), leaf count = 622

\[\left \{c_{1}+\int _{\textit {\_b}}^{x}\frac {-4 \textit {\_a} +2 b -2 \sqrt {4 a y \left (x \right )^{2}+\left (-2 \textit {\_a} +b \right )^{2}}}{4 a y \left (x \right )^{2}+\left (2 \textit {\_a} -b \right ) \sqrt {4 a y \left (x \right )^{2}+\left (-2 \textit {\_a} +b \right )^{2}}+\left (-2 \textit {\_a} +b \right )^{2}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (\frac {4 \textit {\_f} a}{-4 \textit {\_f}^{2} a -b^{2}+4 b x -4 x^{2}+\sqrt {4 \textit {\_f}^{2} a +b^{2}-4 b x +4 x^{2}}\, b -2 \sqrt {4 \textit {\_f}^{2} a +b^{2}-4 b x +4 x^{2}}\, x}-\left (\int _{\textit {\_b}}^{x}\frac {-\frac {32 \textit {\_f}^{3} a^{2}}{\sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}}-16 \left (-2 \textit {\_a} +b -\sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}\right ) \textit {\_f} a}{\left (4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}+2 \sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}\, \textit {\_a} -\sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}\, b \right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} = 0, c_{1}+\int _{\textit {\_b}}^{x}\frac {-4 \textit {\_a} +2 b +2 \sqrt {4 a y \left (x \right )^{2}+\left (-2 \textit {\_a} +b \right )^{2}}}{4 a y \left (x \right )^{2}+\left (-2 \textit {\_a} +b \right ) \sqrt {4 a y \left (x \right )^{2}+\left (-2 \textit {\_a} +b \right )^{2}}+\left (-2 \textit {\_a} +b \right )^{2}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (-\frac {4 \textit {\_f} a}{4 \textit {\_f}^{2} a +b^{2}-4 b x +4 x^{2}+\sqrt {4 \textit {\_f}^{2} a +b^{2}-4 b x +4 x^{2}}\, b -2 \sqrt {4 \textit {\_f}^{2} a +b^{2}-4 b x +4 x^{2}}\, x}-\left (\int _{\textit {\_b}}^{x}\frac {\frac {32 \textit {\_f}^{3} a^{2}}{\sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}}-16 \left (-2 \textit {\_a} +b +\sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}\right ) \textit {\_f} a}{\left (4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}-2 \sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}\, \textit {\_a} +\sqrt {4 \textit {\_f}^{2} a +4 \textit {\_a}^{2}-4 \textit {\_a} b +b^{2}}\, b \right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} = 0, y \left (x \right ) = -\frac {b -2 x}{2 \sqrt {-a}}, y \left (x \right ) = \frac {b -2 x}{2 \sqrt {-a}}\right \}\]