ODE No. 431

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

\[ x^2 y'(x)^2-y(x)^4+y(x)^2=0 \] Mathematica : cpu = 0.036977 (sec), leaf count = 111

\[\left \{\left \{y(x)\to \sqrt {\tan ^2\left (c_1-\log (x)\right )+1} \left (-\cot \left (c_1-\log (x)\right )\right )\right \},\left \{y(x)\to \sqrt {\tan ^2\left (c_1-\log (x)\right )+1} \cot \left (c_1-\log (x)\right )\right \},\left \{y(x)\to \sqrt {\tan ^2\left (c_1+\log (x)\right )+1} \left (-\cot \left (c_1+\log (x)\right )\right )\right \},\left \{y(x)\to \sqrt {\tan ^2\left (c_1+\log (x)\right )+1} \cot \left (c_1+\log (x)\right )\right \}\right \}\] Maple : cpu = 1.401 (sec), leaf count = 62

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