Linear First Order Differential Equation - Mixture Problem

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SUMMARY

The discussion focuses on solving a linear first-order differential equation related to a mixture problem, specifically the equation dP/dt + 0.72P = 0. The solution consists of the general solution of the homogeneous part, which is expressed as P = a eλt, and a particular solution where dP/dt = 0, leading to a constant P. The participants confirm the validity of the approach without identifying any flaws in the original solution presented.

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  • Familiarity with homogeneous and inhomogeneous equations
  • Knowledge of exponential functions in differential equations
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  • Study the method of integrating factors for solving linear differential equations
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jdinatale
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The problem and attempt at solution are typed below

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The solution of a linear differential equation as yours is the sum of the general solution of the homogeneous part (dP/dt+0.72P=0) and an arbitrary particular solution of the inhomogeneous equation. That solution can be for which dP/dt=0, that is P=const. Find that constant.
The solution of the homogeneous equation is of the form P=a eλt. Find λ.

ehild
 
ehild said:
The solution of a linear differential equation as yours is the sum of the general solution of the homogeneous part (dP/dt+0.72P=0) and an arbitrary particular solution of the inhomogeneous equation. That solution can be for which dP/dt=0, that is P=const. Find that constant.
The solution of the homogeneous equation is of the form P=a eλt. Find λ.

ehild

Thanks ehild, but I think what would help me is if someone could point out the flaws in my original solution. I'm trying to solve this problem using the method taught in class so I'm hesitant to try something that we haven't learned.

I don't see any mistakes in my work.
 

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