What is the particular solution of the differential equation # dy/dt = -10t+1 # with Initial Condition #y(0)=-5#?
1 Answer
May 4, 2017
# y = -5t^2+t -5 #
Explanation:
We have:
# dy/dt = -10t+1 #
This is a First Order Separable Differential Equation in standard form, so we can "separate the variables" to get:
# int \ dy = int \ -10t+1 \ dt #
Which we can integrate to get:
# y = -5t^2+t + C #
And using the Initial Condition
# -5 = 0+0 + C => C=-5 #
Hence the unique solution is:
# y = -5t^2+t -5 #
