\[ -a y(x)^s-b x^{\frac {r s}{r-s}}+y'(x)^r=0 \] ✓ Mathematica : cpu = 0.751529 (sec), leaf count = 488
DSolve[-(b*x^((r*s)/(r - s))) - a*y[x]^s + Derivative[1][y][x]^r == 0,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {r}{-r x \left (a K[2]^s+b x^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}+s x \left (a K[2]^s+b x^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}+r K[2]}-\int _1^x\left (\frac {a s K[2]^{s-1} \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}-1}}{r K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-s K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-r K[2]}-\frac {r \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}} \left (-\frac {a s^2 K[1] K[2]^{s-1} \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}-1}}{r}+a s K[1] K[2]^{s-1} \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}-1}-r\right )}{\left (r K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-s K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-r K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {r \left (a y(x)^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}}{r K[1] \left (a y(x)^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-s K[1] \left (a y(x)^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-r y(x)}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.293 (sec), leaf count = 60
dsolve(diff(y(x),x)^r-a*y(x)^s-b*x^(r*s/(r-s))=0,y(x))
\[\left (-r +s \right ) \left (\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{x \left (r -s \right ) \left (a \,\textit {\_a}^{s}+b \,x^{\frac {r s}{r -s}}\right )^{\frac {1}{r}}-r \textit {\_a}}d \textit {\_a} \right )+\ln \left (x \right )-c_{1} = 0\]