2.475   ODE No. 475

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

\[ 4 y(x) y'(x)^2+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.118849 (sec), leaf count = 57

\[\left \{\left \{y(x)\to -\frac {1}{2} e^{2 c_1} \sqrt {-2 x+e^{4 c_1}}\right \},\left \{y(x)\to \frac {1}{2} e^{2 c_1} \sqrt {-2 x+e^{4 c_1}}\right \}\right \}\] Maple : cpu = 0.74 (sec), leaf count = 67

\[\left \{y \left (x \right ) = \sqrt {-c_{1} x +c_{1}^{2}}, y \left (x \right ) = \sqrt {c_{1} x +c_{1}^{2}}, y \left (x \right ) = -\sqrt {c_{1} \left (c_{1}+x \right )}, y \left (x \right ) = -\sqrt {-c_{1} x +c_{1}^{2}}, y \left (x \right ) = -\frac {i x}{2}, y \left (x \right ) = \frac {i x}{2}\right \}\]