A second-order Euler equation is one of the formax2y″ + bxy′ + cy = 0 (22)where a, b, c ar...

A second-order Euler equation is one of the form

ax2y″ + bxy′ + cy = 0 (22)

where a, b, c are constants. (a) Show that if x0, then the substitution v = ln x transforms Eq. into the constant-coefficient linear equation

with independent variable v. (b) If the roots r1 and r2 of the characteristic equation of Eq. are real and distinct, conclude that a general solution of the Euler equation in is y(x) = c1rr1 + c2xr2.