2.1303   ODE No. 1303

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

$$y^{″}(x)(a{x}^2+bx+c)+(dx+f)y^{\prime }(x)+gy(x)=0$$ ✗ Mathematica : cpu = 14.2569 (sec), leaf count = 0 , DifferentialRoot result

$$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {g unicode {f818}(unicode {f817})+(unicode {f817} d+f) unicode {f818}'(unicode {f817})+left (a unicode {f817}^2+b unicode {f817}+cright ) unicode {f818}''(unicode {f817})=0,unicode {f818}(0)=c\_1,unicode {f818}'(0)=c\_2right }right )(x)right }right }}$$

✓ Maple : cpu = 0.214 (sec), leaf count = 501

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(\frac{1}{2a}(-a+d+\sqrt{a^2+(-2d-4g)a+d^2}),-\frac{1}{2a}(a-d+\sqrt{a^2+(-2d-4g)a+d^2});\frac{1}{2a^2}(d\sqrt{\frac{-4ca+b^2}{a^2}}a-2af+bd)\frac{1}{\sqrt{\frac{-4ca+b^2}{a^2}}};\frac{1}{8ca-2b^2}((-2a^{2}x-ab)\sqrt{\frac{-4ca+b^2}{a^2}}+4ca-b^2))+\mathit{\_}\mathit{C}\mathit{2}{(2\sqrt{\frac{-4ca+b^2}{a^2}}x{a}^2+\sqrt{\frac{-4ca+b^2}{a^2}}ba-4ca+b^2)}^{\frac{1}{a^2}(a(a-\frac{d}{2})\sqrt{\frac{-4ca+b^2}{a^2}}+af-\frac{bd}{2})\frac{1}{\sqrt{\frac{-4ca+b^2}{a^2}}}}{}_2\text{F}{}_1(\frac{1}{2a^2}(a(a+\sqrt{a^2+(-2d-4g)a+d^2})\sqrt{\frac{-4ca+b^2}{a^2}}+2af-bd)\frac{1}{\sqrt{\frac{-4ca+b^2}{a^2}}},\frac{1}{2a^2}(a(a-\sqrt{a^2+(-2d-4g)a+d^2})\sqrt{\frac{-4ca+b^2}{a^2}}+2af-bd)\frac{1}{\sqrt{\frac{-4ca+b^2}{a^2}}};\frac{1}{2a^2}(4a^2\sqrt{\frac{-4ca+b^2}{a^2}}-d\sqrt{\frac{-4ca+b^2}{a^2}}a+2af-bd)\frac{1}{\sqrt{\frac{-4ca+b^2}{a^2}}};\frac{1}{8ca-2b^2}((-2a^{2}x-ab)\sqrt{\frac{-4ca+b^2}{a^2}}+4ca-b^2))\}$$