Show that the function y axm bxm is the solution of the di

Show that the function y = ax^m + bx^-m is the solution of the differential equation x^2y\"+xy\'-m^2y = 0

y\'\' = (y\')\'

y\' = amx^m-1-mbx^-m-1

y\'\' = am(m-1)x^m-2+m(m+1)bx^-m-2

x²y\'\' = x²* am(m-1)x^m-2+m(m+1)bx^-m-2

xy\' = x(amx^m-1-mbx^-m-1)

-m²*y =-ax^mm² - m²bx^-m

Adding all these we get: 0.

So, The equation y=ax^m+bx^-m satisfies the differential equation.

$Show that the function y = ax^m + bx^-m is the solution of the differential equation x^2y\$