2.389   ODE No. 389

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

\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-(4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+1) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) (4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+1)=0 \] Mathematica : cpu = 0.0441054 (sec), leaf count = 57

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

Maple : cpu = 0.58 (sec), leaf count = 193

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