4—Differential Equations 1174.45 In the equation of problem 17 , make the change of independent variablex= 1/z. Without actually carrying
out the solution of the resulting equation, what can you say about solving it?
4.46 Show that Eq. ( 42 )(c) has the correct valuePn(1) = 1for alln. Note:(1−x^2 ) = (1 +x)(1−x)and you
are examining the pointx= 1.
4.47 Solve for the complete solution of Eq. ( 36 ) for the caseC= 0. For this, don’t use series methods, but get
the closed form solution.
4.48 Derive the condition in Eq. ( 40 ). Which values ofscorrespond to which values of`?