7.17   ODE No. 1590

$$\boxed{{\displaystyle {(x-a)}^5{(x-b)}^5\frac{{\mathrm{d}}^5}{\mathrm{d}{x}^5}y\left(x\right)-cy\left(x\right)=0}}$$

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

Mathematica: cpu = 343.290592 (sec), leaf count = 72 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {(a-unicode {f817})^5 (b-unicode {f817})^5 unicode {f818}^{(5)}(unicode {f817})-c unicode {f818}(unicode {f817})=0,unicode {f818}(0)=c\_1,unicode {f818}'(0)=c\_2,unicode {f818}''(0)=c\_3,unicode {f818}^{(3)}(0)=c\_4,unicode {f818}^{(4)}(0)=c\_5right }right )(x)right }right }}$$

Maple: cpu = 1.794 (sec), leaf count = 1258 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \frac{{\left({\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}\right)}^2\mathit{\_}\mathit{f}+4{\left({\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}\right)}^{2}b-2{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}\mathit{\_}\mathit{f}-4a{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-4b{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}+\mathit{\_}\mathit{f}+4a}{{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}(a^2-2ab+b^2)}(\frac{b(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)a-\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)b){\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}}{{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-1}-\frac{(b{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-a)(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)a-\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)b){\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}}{{({\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-1)}^2})\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}},[\{(-{\mathit{\_}\mathit{f}}^5-10{\mathit{\_}\mathit{f}}^{4}a-10{\mathit{\_}\mathit{f}}^{4}b-35{\mathit{\_}\mathit{f}}^3{a}^2-90{\mathit{\_}\mathit{f}}^{3}ab-35{\mathit{\_}\mathit{f}}^3{b}^2-50{\mathit{\_}\mathit{f}}^2{a}^3-270{\mathit{\_}\mathit{f}}^2{a}^{2}b-270{\mathit{\_}\mathit{f}}^{2}a{b}^2-50{\mathit{\_}\mathit{f}}^2{b}^3-24\mathit{\_}\mathit{f}{a}^4-304\mathit{\_}\mathit{f}{a}^{3}b-624\mathit{\_}\mathit{f}{a}^2{b}^2-304\mathit{\_}\mathit{f}a{b}^3-24\mathit{\_}\mathit{f}{b}^4-96a^{4}b-416a^3{b}^2-416a^2{b}^3-96a{b}^4+c){\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^5+(-10{\mathit{\_}\mathit{f}}^3-60{\mathit{\_}\mathit{f}}^{2}a-60{\mathit{\_}\mathit{f}}^{2}b-105\mathit{\_}\mathit{f}{a}^2-270\mathit{\_}\mathit{f}ab-105\mathit{\_}\mathit{f}{b}^2-50a^3-270a^{2}b-270a{b}^2-50b^3){\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^4+(-15\mathit{\_}\mathit{f}-30a-30b){\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^3+(10\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right){\mathit{\_}\mathit{f}}^2+40\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)\mathit{\_}\mathit{f}a+40\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)\mathit{\_}\mathit{f}b+35\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)a^2+90\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)ab+35\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)b^2){\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^2+(5\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{f}}^2}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)\mathit{\_}\mathit{f}+10\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{f}}^2}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)a+10\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{f}}^2}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)b+10\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right))\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)-15{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^2\mathit{\_}\mathit{f}-30{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^{2}a-30{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^{2}b+\frac{{\mathrm{d}}^3}{\mathrm{d}{\mathit{\_}\mathit{f}}^3}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)-10\frac{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{f}}^2}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)}{\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)}+15\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^3}{{\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^2}=0\},\{\mathit{\_}\mathit{f}=\frac{x^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}-\frac{ax\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}-\frac{bx\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}+\frac{ab\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}-4x,\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)=-\frac{1}{a-b}({(x-b)}^{-1}-{(x-a)}^{-1}){(x^2(\frac{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}{y\left(x\right)}-\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2}{{\left(y\left(x\right)\right)}^2})-x(\frac{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}{y\left(x\right)}-\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2}{{\left(y\left(x\right)\right)}^2})a-x(\frac{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}{y\left(x\right)}-\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2}{{\left(y\left(x\right)\right)}^2})b+(\frac{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}{y\left(x\right)}-\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2}{{\left(y\left(x\right)\right)}^2})ab+2\frac{x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}-\frac{a\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}-\frac{b\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}-4)}^{-1}\},\{x=\frac{b{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-a}{{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-1},y\left(x\right)={\mathrm{e}}^{\int \frac{{\left({\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}\right)}^2\mathit{\_}\mathit{f}+4{\left({\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}\right)}^{2}b-2{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}\mathit{\_}\mathit{f}-4a{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-4b{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}+\mathit{\_}\mathit{f}+4a}{{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}(a^2-2ab+b^2)}(\frac{b(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)a-\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)b){\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}}{{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-1}-\frac{(b{\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-a)(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)a-\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)b){\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}}{{({\mathrm{e}}^{(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})a-(\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})b}-1)}^2})\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}}\}])\}$$