The solution of the previous problem is
A) $y = c _ { 1 } P _ { 1 / 4 } ( x ) + c _ { 2 } P _ { - 1 / 4 } ( x )$
B) $y = c _ { 1 } P _ { 4 } ( x ) + c _ { 2 } P _ { 4 } ( x )$
C) $y = c _ { 1 } J _ { 4 } ( x ) + c _ { 2 } Y _ { 4 } ( x )$
D) $y = c _ { 1 } J _ { 1 / 4 } ( x ) + c _ { 2 } J _ { - 1 / 4 } ( x )$
E) $y = c _ { 1 } J _ { 1 / 16 } ( x ) + c _ { 2 } J _ { - 1 / 16 } ( x )$

Question

Quizplus · Accepted Answer

The correct solution involves Bessel functions of the first kind, $J_{\nu}(x)$, and their general solution for differential equations often involves $J_{\nu}(x)$ and $J_{-\nu}(x)$ for non-integer $\nu$, making option D the correct choice.

The Solution of the Previous Problem Is A) y=c1P1/4(x)+c2P−1/4(x)y = c _ { 1 } P _ { 1 / 4 } ( x ) + c _ { 2 } P _ { - 1 / 4 } ( x )y=c1​P1/4​(x)+c2​P−1/4​(x)

The Solution of the Previous Problem Is
A) $y = c _ { 1 } P _ { 1 / 4 } ( x ) + c _ { 2 } P _ { - 1 / 4 } ( x )$