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Homework Statement
The problem is given as follows:
Solve
dy/dt + y = 0.5, y(t=0)=1
Homework Equations
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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