2.1760   ODE No. 1760

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

$$ay(x)y^{\prime }(x)+f(x)+xy(x)y^{″}(x)+x{y}^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.0778341 (sec), leaf count = 108

$$\{\{y(x)\to -\sqrt{2}\sqrt{{\int }_1^x-K[2{]}^{-a}(c_1+{\int }_1^{K[2]}f(K[1])K[1{]}^{a-1}dK[1])dK[2]+c_2}\},\{y(x)\to \sqrt{2}\sqrt{{\int }_1^x-K[2{]}^{-a}(c_1+{\int }_1^{K[2]}f(K[1])K[1{]}^{a-1}dK[1])dK[2]+c_2}\}\}$$ ✓ Maple : cpu = 0.056 (sec), leaf count = 114

$$\{y\left(x\right)=\frac{\sqrt{2}}{a-1}\sqrt{(a-1)(x^{1-a}\int \frac{x^{a}f\left(x\right)}{x}\mathrm{d}x+x^{1-a}\mathit{\_}\mathit{C}\mathit{1}-\int f\left(x\right)\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{2})},y\left(x\right)=-\frac{\sqrt{2}}{a-1}\sqrt{(a-1)(x^{1-a}\int \frac{x^{a}f\left(x\right)}{x}\mathrm{d}x+x^{1-a}\mathit{\_}\mathit{C}\mathit{1}-\int f\left(x\right)\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{2})}\}$$