2.1302   ODE No. 1302

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

$$\text{A0}y(x)(ax+b)+\text{A1}(ax+b)y^{\prime }(x)+\text{A2}(ax+b{)}^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0871118 (sec), leaf count = 165

$$\left\{\{y(x)\to (-1{)}^{-\frac{\text{A1}}{a\text{A2}}}{(\frac{b}{a}+x)}^{\frac{\text{A1}}{2a\text{A2}}}(\text{A2}(ax+b){)}^{-\frac{\text{A1}}{2a\text{A2}}}{(-\frac{\text{A0}(ax+b)}{a^2\text{A2}})}^{\frac{1}{2}-\frac{\text{A1}}{2a\text{A2}}}(c_1(-1{)}^{\frac{\text{A1}}{a\text{A2}}}{I}_{\frac{\text{A1}}{a\text{A2}}-1}\left(2\sqrt{-\frac{\text{A0}(b+ax)}{a^2\text{A2}}}\right)-c_2{K}_{\frac{\text{A1}}{a\text{A2}}-1}\left(2\sqrt{-\frac{\text{A0}(b+ax)}{a^2\text{A2}}}\right))\}\right\}$$

✓ Maple : cpu = 0.079 (sec), leaf count = 98

$$\{y\left(x\right)={(ax+b)}^{-\frac{-a\mathit{A}\mathit{2}+\mathit{A}\mathit{1}}{2a\mathit{A}\mathit{2}}}({\mathit{Y}}_{\frac{a\mathit{A}\mathit{2}-\mathit{A}\mathit{1}}{a\mathit{A}\mathit{2}}}\left(2\sqrt{\mathit{A}\mathit{0}}\sqrt{\frac{ax+b}{a^2\mathit{A}\mathit{2}}}\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathit{J}}_{\frac{a\mathit{A}\mathit{2}-\mathit{A}\mathit{1}}{a\mathit{A}\mathit{2}}}\left(2\sqrt{\mathit{A}\mathit{0}}\sqrt{\frac{ax+b}{a^2\mathit{A}\mathit{2}}}\right)\mathit{\_}\mathit{C}\mathit{1})\}$$