2.337   ODE No. 337

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

\[ \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)-y(x)=0 \] Mathematica : cpu = 0.214697 (sec), leaf count = 161

\[\left \{\left \{y(x)\to -\sqrt {-2 i x \cosh (c_1)-2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \},\left \{y(x)\to \sqrt {-2 i x \cosh (c_1)-2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \},\left \{y(x)\to -\sqrt {2 i x \cosh (c_1)+2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \},\left \{y(x)\to \sqrt {2 i x \cosh (c_1)+2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \}\right \}\] Maple : cpu = 0.061 (sec), leaf count = 28

\[ \left \{ -{\it \_C1}+{\frac {1}{ \left ( y \left ( x \right ) \right ) ^{2}}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}}+{\frac {x}{ \left ( y \left ( x \right ) \right ) ^{2}}}=0 \right \} \]