8.170   ODE No. 1760

$$\boxed{{\displaystyle xy\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+x{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+ay\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+f\left(x\right)=0}}$$

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

Mathematica: cpu = 11.966520 (sec), leaf count = 104 $$\{\{y(x)\to -\sqrt{2}\sqrt{{\int }_1^{x}K[2{]}^{-a}(-({\int }_1^{K[2]}K[1{]}^{a-1}f(K[1])dK[1]+c_1))dK[2]+c_2}\},\{y(x)\to \sqrt{2}\sqrt{{\int }_1^{x}K[2{]}^{-a}(-({\int }_1^{K[2]}K[1{]}^{a-1}f(K[1])dK[1]+c_1))dK[2]+c_2}\}\}$$

Maple: cpu = 0.063 (sec), leaf count = 114 $$\{y\left(x\right)=\frac{\sqrt{2}}{a-1}\sqrt{(a-1)(x^{1-a}\int \frac{x^{a}f\left(x\right)}{x}\mathrm{d}x+x^{1-a}\mathit{\_}\mathit{C}\mathit{1}-\int f\left(x\right)\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{2})},y\left(x\right)=-\frac{\sqrt{2}}{a-1}\sqrt{(a-1)(x^{1-a}\int \frac{x^{a}f\left(x\right)}{x}\mathrm{d}x+x^{1-a}\mathit{\_}\mathit{C}\mathit{1}-\int f\left(x\right)\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{2})}\}$$