ODE No. 553

\[ a y'(x)^m+b y'(x)^n-y(x)=0 \]

✓ Mathematica : cpu = 0.378077 (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 = 0.066 (sec), leaf count = 36

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

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