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 = 0.0445709 (sec), leaf count = 57

\[\left \{\left \{y(x)\to -\frac {1}{4} e^{x-4 c_1} \left (2 e^{2 c_1}-e^x\right )\right \},\left \{y(x)\to \frac {1}{4} e^{2 c_1+x} \left (e^{2 c_1+x}-2\right )\right \}\right \}\]

Maple : cpu = 0.54 (sec), leaf count = 193

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