How to add a database to a rds database cluster?

[chris-tuncap]

I'm switching from Terraform to CDK using TypeScript. I was able to create a database cluster (Aurora MySQL) with 2 instances. Converting the existing terraform used to create the cluster to CDK was straightforward, however, I'm having a hard time finding documentation on adding databases to the cluster using CDK.

Terraform uses a MySQL Provider to add database to a cluster:

# Configure the MySQL provider
provider "mysql" {
  endpoint = "my-database.example.com:3306"
  username = "app-user"
  password = "app-password"
}

# Create a Database
resource "mysql_database" "app" {
  name = "my_awesome_app"
}

I've searched around trying to find the equivalent CDK construct and process for adding a database to an existing cluster with no luck. Is this possible to do in CDK?

Code to standup a cluster with 2 instances in cdk:

new rds.DatabaseCluster(
    this,
    `db-cluster`,
    {
        clusterIdentifier: `cluster`,
        credentials: rds.Credentials.fromSecret(...),
        engine: rds.DatabaseClusterEngine.auroraMysql({
            version: rds.AuroraMysqlEngineVersion.of(...)
        }),
        instances: 2,
        instanceProps: {
            vpc,
            securityGroups: [dbSecurityGroup],
            instanceType: new ec2.InstanceType(...)
        },
        subnetGroup,
        instanceIdentifierBase: 'instance-',
    })