# What is the general solution of the differential equation # y'' - 10y' +25 = 0#?

##### 1 Answer

Jun 20, 2017

# y = Axe^(5x) + Be^(5x) #

#### Explanation:

We have:

# y'' - 10y' +25 = 0# ..... [A]

This is a Second order linear Homogeneous Differentiation Equation with constant coefficients. The standard approach is to find a solution,

**Complimentary Function**

The associated Auxiliary equation is:

# m^2-10m+25 = 0#

# (m-5)^2 #

Which has repeated real solutions

Thus the solution of the homogeneous equation is:

# y_c = (Ax+B)e^(5x)#

# \ \ \ = Axe^(5x) + Be^(5x) #

Confirming the quoted solution