2.1760   ODE No. 1760

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

$$ay(x)y^{\prime }(x)+f(x)+x{y}^{\prime }(x{)}^2+xy(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0775087 (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 = 0.49 (sec), leaf count = 106

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