How would I solve these differential equations? Thanks so much

Kathleen Rausch

Kathleen Rausch

Answered question


How would I solve these differential equations? Thanks so much for the help!
We also know P0(t)+P1(t)=1

Answer & Explanation

Jimmy Macias

Jimmy Macias

Beginner2022-01-19Added 30 answers

Note that from the equation you have
which gives us P0(t)+P1(t)=0 which gives us P0(t)+P1(t)=c. We are given that c=1. Use this now to eliminate one in terms of the other.
For instance, P1(t)=1P0(t) and hence we get,
Let Y0(t)=e(α+β)tP0(t)Y0(t)
Hence, Y0(t)=αα+βe(α+β)t+k i.e.
Stuart Rountree

Stuart Rountree

Beginner2022-01-20Added 29 answers

Use P0(t)+P1(t)=1 to turn it into
P0(t)=α(α+β)P0(t), which you should be able to solve.


Expert2022-01-24Added 556 answers

There is a general method to solve such equations, if we view them as a linear system of equationy(x)=Ay(x)When A is a matrix with constants, the solution can be written in terms of the exponent matrix eAx.

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