ODE No. 1527

5.79 ODE No. 1527

${(x - a)}^{3} {(x - b)}^{3} \frac{d^{3}}{d x^{3}} y (x) - c y (x) = 0$

Mathematica: cpu = 135.354688 (sec), leaf count = 58 $\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(a-\unicode {f817})^3 (b-\unicode {f817})^3 \unicode {f818}^{(3)}(\unicode {f817})-c \unicode {f818}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3\right \}\right )(x)\right \}\right \}$

Maple: cpu = 0.421 (sec), leaf count = 500 ${y (x) =_C 1 {(x - a)}^{- 2 \frac{b}{a - b}} {(x - b)}^{2 \frac{a}{a - b}} {(b - x)}^{- \frac{R o o t O f ({_Z}^{3} + (- 3 a - 3 b) {_Z}^{2} + (2 a^{2} + 8 a b + 2 b^{2})_Z - 4 b a^{2} - 4 a b^{2} - c, i n d e x = 1)}{a - b}} {(a - x)}^{\frac{R o o t O f ({_Z}^{3} + (- 3 a - 3 b) {_Z}^{2} + (2 a^{2} + 8 a b + 2 b^{2})_Z - 4 b a^{2} - 4 a b^{2} - c, i n d e x = 1)}{a - b}} +_C 2 {(x - a)}^{- 2 \frac{b}{a - b}} {(x - b)}^{2 \frac{a}{a - b}} {(b - x)}^{- \frac{R o o t O f ({_Z}^{3} + (- 3 a - 3 b) {_Z}^{2} + (2 a^{2} + 8 a b + 2 b^{2})_Z - 4 b a^{2} - 4 a b^{2} - c, i n d e x = 2)}{a - b}} {(a - x)}^{\frac{R o o t O f ({_Z}^{3} + (- 3 a - 3 b) {_Z}^{2} + (2 a^{2} + 8 a b + 2 b^{2})_Z - 4 b a^{2} - 4 a b^{2} - c, i n d e x = 2)}{a - b}} +_C 3 {(x - a)}^{- 2 \frac{b}{a - b}} {(x - b)}^{2 \frac{a}{a - b}} {(b - x)}^{- \frac{R o o t O f ({_Z}^{3} + (- 3 a - 3 b) {_Z}^{2} + (2 a^{2} + 8 a b + 2 b^{2})_Z - 4 b a^{2} - 4 a b^{2} - c, i n d e x = 3)}{a - b}} {(a - x)}^{\frac{R o o t O f ({_Z}^{3} + (- 3 a - 3 b) {_Z}^{2} + (2 a^{2} + 8 a b + 2 b^{2})_Z - 4 b a^{2} - 4 a b^{2} - c, i n d e x = 3)}{a - b}}}$

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