2.84   ODE No. 84

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

\[ y'(x)-f(a x+b y(x))=0 \] Mathematica : cpu = 10.3426 (sec), leaf count = 120

\[\text {Solve}\left [c_1=\int _1^{y(x)} -\frac {(b f(b K[2]+a x)+a) \int _1^x \frac {a b^2 f'(a K[1]+b K[2])}{(b f(a K[1]+b K[2])+a)^2} \, dK[1]+b}{b f(b K[2]+a x)+a} \, dK[2]+\int _1^x \frac {b f(a K[1]+b y(x))}{b f(a K[1]+b y(x))+a} \, dK[1],y(x)\right ]\]

Maple : cpu = 0.037 (sec), leaf count = 37

\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( f \left ( {\it \_a}\,b \right ) b+a \right ) ^{-1}{d{\it \_a}}b-x+{\it \_C1} \right ) b-ax}{b}} \right \} \]