# 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 #