(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is given as follows:

Solve

dy/dt + y = 0.5, y(t=0)=1

2. Relevant equations

3. The attempt at a solution

I separate the y terms from the t terms, which gives me

dy(-y+0.5)=dt

I integrate both sides to get

-ln(-y+0.5)=t+C

C is the constant, I combine the constants from both sides to one value.

Multiplying both sides by the negative,

ln(-y+0.5)=-t-C

Now i e both sides

-y+0.5=e^(-t-C)

Therefore I can simplify to y=e^(-t-C)+0.5, which is my solution

Since y(0)=1,

e^(-C) = 0.5

I don't know what exactly I am supposed to do with that...

Was my answer correct?

Please advise, Thank you!

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# Homework Help: Solve First order linear differential equation, initial conditions

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