2.1054   ODE No. 1054

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

$$(ax+b)y^{\prime }(x)+y(x)(cx+d)+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0494446 (sec), leaf count = 172

$$\left\{\{y(x)\to c_1{e}^{\frac{cx}{a}-\frac{a{x}^2}{2}-bx}{H}_{\frac{-a^3+a^{2}d-abc+c^2}{a^3}}(\frac{ab-2c}{\sqrt{2}{a}^{3/2}}+\frac{\sqrt{a}x}{\sqrt{2}})+c_2{e}^{\frac{cx}{a}-\frac{a{x}^2}{2}-bx}{}_1{F}_1(-\frac{-a^3+d{a}^2-bca+c^2}{2a^3};\frac{1}{2};{(\frac{ab-2c}{\sqrt{2}{a}^{3/2}}+\frac{\sqrt{a}x}{\sqrt{2}})}^2)\}\right\}$$

✓ Maple : cpu = 0.053 (sec), leaf count = 105

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{cx}{a}}\mathit{M}(\frac{d{a}^2-abc+c^2}{2a^3},\frac{1}{2},-\frac{{(a^{2}x+ab-2c)}^2}{2a^3})+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{cx}{a}}\mathit{U}(\frac{d{a}^2-abc+c^2}{2a^3},\frac{1}{2},-\frac{{(a^{2}x+ab-2c)}^2}{2a^3})\}$$