2.550   ODE No. 550

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

$$-ay(x{)}^s-b{x}^{\frac{rs}{r-s}}+y^{\prime }(x{)}^r=0$$ ✓ Mathematica : cpu = 0.718201 (sec), leaf count = 488

$$\text{Solve}[{\int }_1^{y(x)}(\frac{r}{-rx{(aK[2{]}^s+b{x}^{\frac{rs}{r-s}})}^{\frac{1}{r}}+sx{(aK[2{]}^s+b{x}^{\frac{rs}{r-s}})}^{\frac{1}{r}}+rK[2]}-{\int }_1^x(\frac{asK[2{]}^{s-1}{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}-1}}{rK[1]{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}-sK[1]{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}-rK[2]}-\frac{r{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}(-\frac{a{s}^{2}K[1]K[2{]}^{s-1}{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}-1}}{r}+asK[1]K[2{]}^{s-1}{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}-1}-r)}{{(rK[1]{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}-sK[1]{(aK[2{]}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}-rK[2])}^2})dK[1])dK[2]+{\int }_1^x\frac{r{(ay(x{)}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}}{rK[1]{(ay(x{)}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}-sK[1]{(ay(x{)}^s+bK[1{]}^{\frac{rs}{r-s}})}^{\frac{1}{r}}-ry(x)}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.762 (sec), leaf count = 60

$$\{(-r+s){\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{(x(r-s)\sqrt[r]{a{\mathit{\_}\mathit{a}}^s+b{x}^{\frac{rs}{r-s}}}-r\mathit{\_}\mathit{a})}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$