Design an XML schema $($XSD$)$ for a student database that includes the following information:

$1)$ Student Details

$-$Student ID

$-$First Name

$-$Last Name

$-$Email

$-$Date of Birth

$2)$ Course Enrollment

$-$Course ID

$-$Course Name

$-$Semester

$-$Grade

Your schema should use complex types to define the structure of the student and course data. Include any necessary elements, attributes, and constraints to ensure the XML document is well$-$formed and valid.

Provide the complete XSD code for the schema, and then use an XML validator $($such as an online XSD validator$)$ to demonstrate that your schema is valid.

Alternatively, you can write a script in a programming language of your choice $($e$.$g$.,$ Python, Java, or JavaScript$)$ to validate an XML document against your designed schema.

The goal is to create a comprehensive XML schema that can be used to store and manage student information, course enrollment, and grades in a structured and organized manner.