# What is a solution to the differential equation #(dy/dx) +5y = 9#?

##### 1 Answer

Nov 21, 2016

#### Explanation:

This is a First Order Separable Differential Equation.

We can isolate the variables as follows;

# dy/dx + 5y = 9 #

# :. dy/dx = 9 - 5y#

Separating the variable gives us:

# :. int 1/(9 - 5y)dy = int dx#

# :. -int 1/(5y-9)dy = int dx#

Integrating gives us:

# -1/5 ln|5y-9| = x + C #

# :. ln|5y-9| = -5x -5C #

# :. 5y-9 = e^(-5x -5C) #

# :. 5y-9 = e^(-5x)e^( -5C) #

# :. 5y-9 = Ae^(-5x) #

# :. 5y = 9 + A/5e^(-5x) #

# :. y = 9/5 + Be^(-5x) #

**Verification of Solution:**

# y = 9/5 + Be^(-5x) #

# y = -5Be^(-5x) #

So,