Differential Equations: Find the Solutions and Limiting Factos

[Northbysouth]

Homework Statement

Determine the solution and limiting factor

(t+1)y' + y = 6

y(1) = -2

Homework Equations

The Attempt at a Solution

So I started off by isolating y'

y' + y/(t+1) = 6(t+1)

Then I found u(t)

u(t) = e^{∫ t+1 dt} = e^{t2/2 +t}

y' =(e^{t2/2 +t}) = y(e^{t2/2 +t}) = 6(e^{t2/2 +t})/(t+1)

The difficulty I'm having is integrating 6(e^{t2/2 +t})/(t+1)

u-substitution doesn't help. Suggestions are appreciated

 

[LCKurtz]

Homework Statement

Determine the solution and limiting factor

(t+1)y' + y = 6

y(1) = -2

Homework Equations

The Attempt at a Solution

So I started off by isolating y'

y' + y/(t+1) = 6(t+1)

Then I found u(t)

u(t) = e^{∫ t+1 dt}

That should be $u(t) = e^{\int \frac 1 {t+1}}\, dt$.

 

[Northbysouth]

Ahh, thank you.

Can you explain to me what is meant by the limiting factor? Is it the largest range of t values for the given information of y(1) = -2?

 

[LCKurtz]

Ahh, thank you.

Can you explain to me what is meant by the limiting factor? Is it the largest range of t values for the given information of y(1) = -2?

I am not familiar with the term "limiting factor". Perhaps it refers to disallowed values of t in your answer.