2.488   ODE No. 488

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

\[ 4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0 \] Mathematica : cpu = 0.345834 (sec), leaf count = 85

\[\left \{\left \{y(x)\to -\frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a}\right \},\left \{y(x)\to \frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a}\right \}\right \}\] Maple : cpu = 0.5 (sec), leaf count = 111

\[\left \{y \left (x \right ) = -2 \sqrt {a x}, y \left (x \right ) = 2 \sqrt {a x}, y \left (x \right ) = -\frac {\sqrt {-16 a^{4}+32 a^{3} x +8 c_{1} a x -c_{1}^{2}+\left (-16 x^{2}+8 c_{1}\right ) a^{2}}}{4 a}, y \left (x \right ) = \frac {\sqrt {-16 a^{4}+32 a^{3} x +8 c_{1} a x -c_{1}^{2}+\left (-16 x^{2}+8 c_{1}\right ) a^{2}}}{4 a}\right \}\]