2.1407   ODE No. 1407

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

$$y^{″}(x)=-y^{\prime }(x)(\frac{\text{b1}(-\text{al1}-\text{bl1}+1)}{\text{b1}x-\text{a1}}+\frac{\text{b2}(-\text{al2}-\text{bl2}+1)}{\text{b2}x-\text{a2}}+\frac{\text{b3}(-\text{al3}-\text{bl3}+1)}{\text{b3}x-\text{a3}})-\frac{y(x)(\frac{\text{al1}\text{bl1}(\text{a1}\text{b2}-\text{a2}\text{b1})(\text{a3}\text{b1}-\text{a1}\text{b3})}{\text{b1}x-\text{a1}}+\frac{\text{al2}\text{bl2}(\text{a1}\text{b2}-\text{a2}\text{b1})(\text{a2}\text{b3}-\text{a3}\text{b2})}{\text{b2}x-\text{a2}}+\frac{\text{al3}\text{bl3}(\text{a3}\text{b1}-\text{a1}\text{b3})(\text{a2}\text{b3}-\text{a3}\text{b2})}{\text{b3}x-\text{a3}})}{(\text{b1}x-\text{a1})(\text{b2}x-\text{a2})(\text{b3}x-\text{a3})}$$ ✓ Mathematica : cpu = 88.7641 (sec), leaf count = 2002

$$\left\{\{y(x)\to {(x-\frac{\text{a2}}{\text{b2}})}^{\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})}{(x-\frac{\text{a3}}{\text{b3}})}^{\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})}{c}_1\text{HeunG}[\frac{\frac{\text{a1}}{\text{b1}}-\frac{\text{a3}}{\text{b3}}}{\frac{\text{a1}}{\text{b1}}-\frac{\text{a2}}{\text{b2}}},\frac{\frac{\text{a1}(\frac{1}{2}(-\text{al1}-\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+1)(\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2}))}{\text{b1}}+\frac{\text{a3}(\frac{1}{4}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\frac{1}{2}(\text{al2}+\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})-1)(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})-\frac{1}{4}(\text{al3}+\text{bl3}-\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2}))}{\text{b3}}+\frac{\text{a2}(\frac{1}{4}(-\text{al2}-\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})(\text{al2}+\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{4}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})(\frac{1}{2}(\text{al3}+\text{bl3}-\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})-1))}{\text{b2}}+\frac{1}{2}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})(\frac{\text{a3}(\frac{1}{2}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al2}+\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})-1)}{\text{b3}}+\frac{\text{a2}(\frac{1}{2}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}-\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})-1)}{\text{b2}}+\frac{\text{a1}(-\text{al1}-\text{bl1}+\frac{1}{2}(-\text{al2}-\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(-\text{al3}-\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2}+2)}{\text{b1}})}{\frac{\text{a1}}{\text{b1}}-\frac{\text{a2}}{\text{b2}}},\frac{1}{2}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2}),\frac{1}{2}(-\text{al1}-\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(-\text{al2}-\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(-\text{al3}-\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})+2,\frac{1}{2}(-\text{al1}-\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+1,\frac{1}{2}(-\text{al2}-\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+1,\frac{\frac{\text{a1}}{\text{b1}}-x}{\frac{\text{a1}}{\text{b1}}-\frac{\text{a2}}{\text{b2}}}]{(x-\frac{\text{a1}}{\text{b1}})}^{\frac{1}{2}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})}+{(x-\frac{\text{a2}}{\text{b2}})}^{\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})}{(x-\frac{\text{a3}}{\text{b3}})}^{\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})}{c}_2\text{HeunG}[\frac{\frac{\text{a1}}{\text{b1}}-\frac{\text{a3}}{\text{b3}}}{\frac{\text{a1}}{\text{b1}}-\frac{\text{a2}}{\text{b2}}},\frac{\frac{\text{a1}(\frac{1}{2}(-\text{al1}-\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+1)(\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2}))}{\text{b1}}+\frac{\text{a3}(\frac{1}{4}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\frac{1}{2}(\text{al2}+\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})-1)(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})-\frac{1}{4}(\text{al3}+\text{bl3}-\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2}))}{\text{b3}}+\frac{\text{a2}(\frac{1}{4}(-\text{al2}-\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})(\text{al2}+\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{4}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})(\frac{1}{2}(\text{al3}+\text{bl3}-\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})-1))}{\text{b2}}+\frac{1}{2}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})(\frac{\text{a3}(\frac{1}{2}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al2}+\text{bl2}+\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})-1)}{\text{b3}}+\frac{\text{a2}(\frac{1}{2}(\text{al1}+\text{bl1}-\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}-\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})-1)}{\text{b2}}+\frac{\text{a1}(-\text{al1}-\text{bl1}+\frac{1}{2}(-\text{al2}-\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(-\text{al3}-\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2}+2)}{\text{b1}})}{\frac{\text{a1}}{\text{b1}}-\frac{\text{a2}}{\text{b2}}},\frac{1}{2}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\text{al3}+\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2}),\frac{1}{2}(-\text{al1}-\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(-\text{al2}-\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(-\text{al3}-\text{bl3}+\sqrt{{\text{al3}}^2+6\text{bl3}\text{al3}+{\text{bl3}}^2})+2,\frac{1}{2}(-\text{al1}-\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+\frac{1}{2}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})+1,\frac{1}{2}(-\text{al2}-\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+\frac{1}{2}(\text{al2}+\text{bl2}-\sqrt{{\text{al2}}^2+6\text{bl2}\text{al2}+{\text{bl2}}^2})+1,\frac{\frac{\text{a1}}{\text{b1}}-x}{\frac{\text{a1}}{\text{b1}}-\frac{\text{a2}}{\text{b2}}}]{(x-\frac{\text{a1}}{\text{b1}})}^{\frac{1}{2}(\text{al1}+\text{bl1}+\sqrt{{\text{al1}}^2+6\text{bl1}\text{al1}+{\text{bl1}}^2})}\}\right\}$$ ✓ Maple : cpu = 1.664 (sec), leaf count = 2607

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