2.389   ODE No. 389

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

\[ y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0 \] Mathematica : cpu = 0.0636879 (sec), leaf count = 57

\[\left \{\left \{y(x)\to -\frac {1}{4} e^{x-4 c_1} \left (-e^x+2 e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{4} e^{x+2 c_1} \left (-2+e^{x+2 c_1}\right )\right \}\right \}\] Maple : cpu = 2.411 (sec), leaf count = 71

\[ \left \{ y \left ( x \right ) =-{\frac {1}{4}},y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( - \left ( {{\rm e}^{x}} \right ) ^{2}\sqrt {-{\frac {{\it \_C1}}{ \left ( {{\rm e}^{x}} \right ) ^{2}}}}+{\it \_C1} \right ) {\frac {1}{\sqrt {-{\frac {{\it \_C1}}{ \left ( {{\rm e}^{x}} \right ) ^{2}}}}}}},y \left ( x \right ) =-{\frac {1}{{\it \_C1}} \left ( \left ( {{\rm e}^{x}} \right ) ^{2}\sqrt {-{\frac {{\it \_C1}}{ \left ( {{\rm e}^{x}} \right ) ^{2}}}}+{\it \_C1} \right ) {\frac {1}{\sqrt {-{\frac {{\it \_C1}}{ \left ( {{\rm e}^{x}} \right ) ^{2}}}}}}} \right \} \]