2.54   ODE No. 54

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

$$-a^{n}f(x{)}^{1-n}{g}^{\prime }(x)y(x{)}^n-\frac{y(x)f^{\prime }(x)}{f(x)}-f(x)g^{\prime }(x)+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.117056 (sec), leaf count = 74

$$\text{Solve}[y(x){(a^{n}f(x{)}^{-n})}^{\frac{1}{n}}{}_2{F}_1(1,\frac{1}{n};1+\frac{1}{n};-{({(a^{n}f(x{)}^{-n})}^{\frac{1}{n}}y(x))}^n)=f(x)g(x){(a^{n}f(x{)}^{-n})}^{\frac{1}{n}}+c_1,y(x)]$$

✓ Maple : cpu = 0.174 (sec), leaf count = 42

$$\{\mathit{\_}\mathit{C}\mathit{1}+\frac{y\left(x\right)}{f\left(x\right)}{}_2\text{F}{}_1(1,n^{-1};\frac{n+1}{n};-{\left(\frac{ay\left(x\right)}{f\left(x\right)}\right)}^n)-g\left(x\right)=0\}$$