2.127   ODE No. 127

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

$$x{y}^{\prime }(x)-y(x)f(x^{a}y(x{)}^b)=0$$ ✓ Mathematica : cpu = 0.232468 (sec), leaf count = 186

$$\text{Solve}[{\int }_1^{y(x)}(-\frac{b}{(a+bf(x^{a}K[2{]}^b))K[2]}-{\int }_1^x(\frac{b^{2}K[1{]}^{a-1}K[2{]}^{b-1}{f}^{\prime }(K[1{]}^{a}K[2{]}^b)}{a+bf(K[1{]}^{a}K[2{]}^b)}-\frac{b^{3}f(K[1{]}^{a}K[2{]}^b)K[1{]}^{a-1}K[2{]}^{b-1}{f}^{\prime }(K[1{]}^{a}K[2{]}^b)}{{(a+bf(K[1{]}^{a}K[2{]}^b))}^2})dK[1])dK[2]+{\int }_1^x\frac{bf(K[1{]}^{a}y(x{)}^b)}{(a+bf(K[1{]}^{a}y(x{)}^b))K[1]}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.091 (sec), leaf count = 39

$$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{1}{(f\left(x^a{\mathit{\_}\mathit{a}}^b\right)b+a)\mathit{\_}\mathit{a}}\mathrm{d}\mathit{\_}\mathit{a}-\frac{\ln \left(x\right)}{b}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$