2.375   ODE No. 375

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

\[ a y'(x)+b x+y'(x)^2=0 \] Mathematica : cpu = 0.0301193 (sec), leaf count = 71

\[\left \{\left \{y(x)\to \frac {1}{2} \left (-\frac {\left (a^2-4 b x\right )^{3/2}}{6 b}-a x\right )+c_1\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {\left (a^2-4 b x\right )^{3/2}}{6 b}-a x\right )+c_1\right \}\right \}\] Maple : cpu = 0.023 (sec), leaf count = 49

\[ \left \{ y \left ( x \right ) =-{\frac {ax}{2}}-{\frac {1}{12\,b} \left ( {a}^{2}-4\,bx \right ) ^{{\frac {3}{2}}}}+{\it \_C1},y \left ( x \right ) =-{\frac {ax}{2}}+{\frac {1}{12\,b} \left ( {a}^{2}-4\,bx \right ) ^{{\frac {3}{2}}}}+{\it \_C1} \right \} \]