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,