2.1468   ODE No. 1468

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

$$2(2a+4x^2-1)y^{\prime }(x)-8axy(x)+y^{(3)}(x)-6x{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0856028 (sec), leaf count = 57

$$\left\{\{y(x)\to c_2{H}_{\frac{a}{2}}(x){}_1{F}_1(-\frac{a}{4};\frac{1}{2};x^2)+c_1{H}_{\frac{a}{2}}(x){}^2+c_3{}_1{F}_1(-\frac{a}{4};\frac{1}{2};x^2){}^2\}\right\}$$

✓ Maple : cpu = 0.138 (sec), leaf count = 64

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\left(\mathit{M}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)\right)}^2{x}^2+\mathit{\_}\mathit{C}\mathit{2}{\left(\mathit{U}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)\right)}^2{x}^2+\mathit{\_}\mathit{C}\mathit{3}\mathit{M}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)x^2\mathit{U}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)\}$$