ODE No. 1302

4.302 ODE No. 1302

$A 2 {(a x + b)}^{2} \frac{d^{2}}{d x^{2}} y (x) + A 1 (a x + b) \frac{d}{d x} y (x) + A 0 (a x + b) y (x) = 0$

Mathematica: cpu = 0.084011 (sec), leaf count = 243 ${{y (x) \to c_{1} {(\frac{2 b}{a} + 2 x)}^{\frac{A1}{2 a A2}} (2 a A2 x + 2 A2 b)^{- \frac{A1}{2 a A2}} {(- \frac{A0 (\frac{b}{a} + x)}{a A2})}^{\frac{1}{2} - \frac{A1}{2 a A2}} I_{\frac{A1}{a A2} - 1} (2 \sqrt{- \frac{A0 (\frac{b}{a} + x)}{a A2}}) + c_{2} (- 1)^{1 - \frac{A1}{a A2}} {(\frac{2 b}{a} + 2 x)}^{\frac{A1}{2 a A2}} (2 a A2 x + 2 A2 b)^{- \frac{A1}{2 a A2}} {(- \frac{A0 (\frac{b}{a} + x)}{a A2})}^{\frac{1}{2} - \frac{A1}{2 a A2}} K_{\frac{A1}{a A2} - 1} (2 \sqrt{- \frac{A0 (\frac{b}{a} + x)}{a A2}})}}$

Maple: cpu = 0.046 (sec), leaf count = 117 ${y (x) =_C 1 {(a x + b)}^{- \frac{- a A 2 + A 1}{2 a A 2}} J_{\frac{a A 2 - A 1}{a A 2}} (2 \sqrt{A 0} \sqrt{\frac{a x + b}{a^{2} A 2}}) +_C 2 {(a x + b)}^{- \frac{- a A 2 + A 1}{2 a A 2}} Y_{\frac{a A 2 - A 1}{a A 2}} (2 \sqrt{A 0} \sqrt{\frac{a x + b}{a^{2} A 2}})}$

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