The solution of the differential equation x^2y"-5xy'+5y=0 is select the correct answer. (a)y=c1x+c2x^2, (b)y=c1xcoslnx+c2x^2sinlnx, (c)y=c1xcos2lnx+c2x^2sin2lnx, (d) c1x^(5+rad5/2)+c2x^(5-rad5/2) , or (e)y=c1e^2x+c2xe^2xsinx

Step-by-step explanation:

The given second order homogeneous Cauchy-Euler ordinary differential equation is

The corresponding auxiliary equation is given by:

where a=1, b=-5, c=5

We substitute the coefficients into the auxiliary equation to obtain:

The auxiliary equation has two distinct real roots. The general solution to the corresponding differential equation is of the form:

We substitute the values to get:

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.