- #1

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- Homework Statement
- See attached problem and ms guide

- Relevant Equations
- linear first order ode

My approach for part (a),

##\dfrac{dp}{dt}+P(t)=100##

I.f=## e^{\int 1 dt} = e^t##

Therefore,

##(e^t p)^{'}=100e^t##

##e^tp=\int 100e^t dt##

##e^tp=100e^t+k## Applying initial condition, ##p(0)=2000##

##2000=100+k##

##k=1900##

Therefore,

##e^tp=100e^t+1900##

##p=100+1900e^{-t}##

More insight is welcome guys...