What is the particular solution of the differential equation $dy/dt = -10t+1$ with Initial Condition $y(0)=-5$ ?

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Answer 1 · 2017-05-04T10:49:27

$y = -5t^2+t -5$

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 $y(0)=-5$ we have:

$-5 = 0+0 + C => C=-5$

Hence the unique solution is:

$y = -5t^2+t -5$

What is the particular solution of the differential equation dy/dt = -10t+1 dy/dt = -10t+1 with Initial Condition y(0)=-5y(0)=-5?