2.169   ODE No. 169

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

\[ (a x+b)^2 y'(x)+y(x)^3 (a x+b)+c y(x)^2=0 \] Mathematica : cpu = 2.57346 (sec), leaf count = 110

\[\text {Solve}\left [-\frac {c}{\sqrt {-a (a x+b)^2}}=\frac {2 \exp \left (-\frac {(a (a x+b)+c y(x))^2}{2 a y(x)^2 (a x+b)^2}\right )}{2 c_1-\sqrt {2 \pi } \text {erfi}\left (\frac {a (a x+b)+c y(x)}{\sqrt {2} y(x) \sqrt {-a (a x+b)^2}}\right )},y(x)\right ]\]

Maple : cpu = 0.158 (sec), leaf count = 153

\[ \left \{ {\frac {1}{2} \left ( \left ( \sqrt {2}\sqrt {\pi }{\it Erf} \left ( {\frac { \left ( cy \left ( x \right ) +a \left ( ax+b \right ) \right ) \sqrt {2}}{2\, \left ( ax+b \right ) y \left ( x \right ) }{\frac {1}{\sqrt {a}}}} \right ) {{\rm e}^{{\frac { \left ( cy \left ( x \right ) +a \left ( ax+b \right ) \right ) ^{2}}{2\, \left ( y \left ( x \right ) \right ) ^{2} \left ( ax+b \right ) ^{2}a}}}}ac+2\, \left ( ax+b \right ) {a}^{3/2} \right ) {{\rm e}^{-{\frac { \left ( \left ( ax+b+c \right ) y \left ( x \right ) +a \left ( ax+b \right ) \right ) \left ( \left ( -ax-b+c \right ) y \left ( x \right ) +a \left ( ax+b \right ) \right ) }{2\, \left ( y \left ( x \right ) \right ) ^{2} \left ( ax+b \right ) ^{2}a}}}}+2\,{\it \_C1}\,{a}^{5/2} \right ) {a}^{-{\frac {5}{2}}}}=0 \right \} \]