3.571   ODE No. 571

$$\boxed{{\displaystyle a{x}^{n}f\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)+x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.102013 (sec), leaf count = 114 $$\text{Solve}[\{y(x)=af(\text{K}\mathrm{\$}\text{1487621})x^n+\text{K}\mathrm{\$}\text{1487621}x,x=(nf(\text{K}\mathrm{\$}\text{1487621}{)}^{\frac{1}{n}-1}({\int }_1^{\text{K}\mathrm{\$}\text{1487621}}-\frac{f(K[1]{)}^{\frac{n-1}{n}-1}}{an}dK[1])-f(\text{K}\mathrm{\$}\text{1487621}{)}^{\frac{1}{n}-1}({\int }_1^{\text{K}\mathrm{\$}\text{1487621}}-\frac{f(K[1]{)}^{\frac{n-1}{n}-1}}{an}dK[1])+c_{1}f(\text{K}\mathrm{\$}\text{1487621}{)}^{\frac{1}{n}-1}){}^{\frac{1}{n-1}}\},\{y(x),\text{K}\mathrm{\$}\text{1487621}\}]$$

Maple: cpu = 0.203 (sec), leaf count = 199 $$\{[y\left(\mathit{\_}\mathit{T}\right)=a{\left({(-\frac{1}{af\left(\mathit{\_}\mathit{T}\right)n}(-\mathit{\_}\mathit{C}\mathit{1}an+\int {\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{-n^{-1}}\mathrm{d}\mathit{\_}\mathit{T}n-\int {\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{-n^{-1}}\mathrm{d}\mathit{\_}\mathit{T}))}^{{(n-1)}^{-1}}{\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{\frac{1}{n(n-1)}}\right)}^{n}f\left(\mathit{\_}\mathit{T}\right)+\mathit{\_}\mathit{T}{(-\frac{1}{af\left(\mathit{\_}\mathit{T}\right)n}(-\mathit{\_}\mathit{C}\mathit{1}an+\int {\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{-n^{-1}}\mathrm{d}\mathit{\_}\mathit{T}n-\int {\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{-n^{-1}}\mathrm{d}\mathit{\_}\mathit{T}))}^{{(n-1)}^{-1}}{\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{\frac{1}{n(n-1)}},x\left(\mathit{\_}\mathit{T}\right)={(-\frac{1}{af\left(\mathit{\_}\mathit{T}\right)n}(-\mathit{\_}\mathit{C}\mathit{1}an+\int {\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{-n^{-1}}\mathrm{d}\mathit{\_}\mathit{T}n-\int {\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{-n^{-1}}\mathrm{d}\mathit{\_}\mathit{T}))}^{{(n-1)}^{-1}}{\left(f\left(\mathit{\_}\mathit{T}\right)\right)}^{\frac{1}{n(n-1)}}]\}$$