Separation of Variables| Elementary Differential Equations|dela Fuente, Feliciano, and Uy|Example 2

Find the complete solution of the following differential equation: 

L\:dI+RI\:dt=0\:\left(L\:and\:R\:are\:constants\right).

SOLUTION:

Write the given differential equation as

\frac{dI}{I}+\frac{R}{L}dt=0

\int \:\frac{dI}{I}+\int \:\frac{R}{L}dt=\int \:0

ln\:I+\frac{R}{L}t=C

ln\:I=C-kt\:\:\:\:\:\left(k=\frac{R}{L}\right)

I=C_1e^{-kt}\:\:\:\:\:\:\:\:\left(C_1=e^C\right)

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