2.1756   ODE No. 1756

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

$$ay(x)y^{″}(x)+b{y}^{\prime }(x{)}^2-\frac{y(x)y^{\prime }(x)}{\sqrt{c^2+x^2}}=0$$ ✓ Mathematica : cpu = 0.284845 (sec), leaf count = 111

$$\left\{\{y(x)\to c_2(-a^2(x{(\sqrt{c^2+x^2}+x)}^{\frac{1}{a}}+c_1)+a{(\sqrt{c^2+x^2}+x)}^{\frac{1}{a}}(\sqrt{c^2+x^2}-bx)+b\sqrt{c^2+x^2}{(\sqrt{c^2+x^2}+x)}^{\frac{1}{a}}+c_1){}^{\frac{a}{a+b}}\}\right\}$$

✓ Maple : cpu = 0.659 (sec), leaf count = 79

$$\{y\left(x\right)={\left({\left(\frac{a}{a+b}{(-\mathit{\_}\mathit{C}\mathit{1}\sqrt[a]{2}{x}^{a^{-1}+1}{}_2\text{F}{}_1(-\frac{1}{2a},-\frac{1}{2a}-\frac{1}{2};1-a^{-1};-\frac{c^2}{x^2}){(-a^{-1}-1)}^{-1}+\mathit{\_}\mathit{C}\mathit{2})}^{-1}\right)}^{\frac{a}{a+b}}\right)}^{-1}\}$$