$\"\"$

The function is $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Verify the differential equation $\"\"$ and initial condition $\"\"$ correspond to the function $\"\"$ .

Consider $\"\"$ .

Rewrite the above equation.

$\"\"$

Substitute $\"\"$ in the above equation.

$\"\"$

Hence $\"\"$ .

$\"\"$ correspond to the function $\"\"$ .

Substitute $\"\"$ in above function.

$\"\"$

The initial condition $\"\"$ correspond to the function $\"\"$ .

The differential equation $\"\"$ and initial condition $\"\"$ is a solution of the function $\"\"$ .

$\"\"$

The differential equation $\"\"$ and initial condition $\"\"$ is a solution of the function $\"\"$ .