# Differential equation, Particular solution

The amount of money M in an account is increasing at the rate of 9% per year.

(a) Write a differential equation that describes the amount at any time t.

(b) Find the particular solution for M, given that the account begins with $2,000 in it.

(c) When will there be $24,000 in the account?

https://brainmass.com/math/calculus-and-analysis/writing-differential-equation-finding-particular-solution-312741

#### Solution Preview

a) dM/dt = 0.09M

b) dM/dt = 0.09M

dM/M = 0.09 dt

Upon integration, we get ln M = 0.09t + ...

#### Solution Summary

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2. Find the particular solution of the differential equation that satisfies the boundary condition.

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