Step 1:

The function is $\"\"$ .

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

$\"\"$

Step 2:

Verify the differential equation $\"\"$ and initial condition $\"\"$ .

Consider $\"\"$ .

Rewrite the expression.

$\"\"$

$\"\"$ ( Since $\"\"$ )

$\"\"$

The differential equation $\"\"$ is verified.

$\"\"$

Substitute $\"\"$ in above function.

$\"\"$

The initial condition $\"\"$ is verified.

Solution :

The differential equation $\"\"$ is verified.

The initial condition $\"\"$ is verified.