# 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

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

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

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

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

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