ODE No. 553

\[ a y'(x)^m+b y'(x)^n-y(x)=0 \] Mathematica : cpu = 0.238174 (sec), leaf count = 56

DSolve[-y[x] + a*Derivative[1][y][x]^m + b*Derivative[1][y][x]^n == 0,y[x],x]
 

\[\text {Solve}\left [\left \{x=\frac {a m K[1]^{m-1}}{m-1}+\frac {b n K[1]^{n-1}}{n-1}+c_1,y(x)=a K[1]^m+b K[1]^n\right \},\{y(x),K[1]\}\right ]\] Maple : cpu = 0.073 (sec), leaf count = 36

dsolve(a*diff(y(x),x)^m+b*diff(y(x),x)^n-y(x)=0,y(x))
 

\[y \left (x \right ) = 0\]