Using the indicated substitutions x^2=z, find a general solution of x^2y\'\'+ xy

Question

Using the indicated substitutions x^2=z, find a general solution of x^2y''+ xy'+4(x^4-v^2)y=0 in terms of Jv and J-v.                                                          

                                
                                 A.)  y=c1J2(x)+c2J-2(x)
                                 
                                 B.)  y=c1Jv(x) + c2J-v(x)
                                 
                                 C.)  y=c1J1/4(x)-c2J-1/4(x)
                                 
                                  D.)  y=c1Jv(x^2)+c2J-v(x^2)                                                  

Explanation / Answer

B.)  y=c1Jv(x) + c2J-v(x)

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