Add inline css to theme

According to Codex, this function accepts 2 arguments:

<?php wp_add_inline_style( $handle, $data ); ?>

Take a look at this example:

function my_inline_css() {
    wp_enqueue_style(
        'custom-style',
        get_template_directory_uri() . '/css/custom_script.css'
    );
        $btn_color = esc_attr( get_theme_mod( 'my-custom-color' ) ); 
        $custom_css = "
                .btn-default{
                        background-color: {$btn_color};
                }";
        wp_add_inline_style( 'custom-style', $my_custom_css );
}
add_action( 'wp_enqueue_scripts', 'my_inline_css' );

You should have an option in your theme to specify the background-color and then output it using wp_add_inline_style().

You also have other options, such as hooking into wp_head():

function my_inline_css($btn_color) { 
    if ( !empty($btn_color) ) {  ?> 
        .btn-default { background-color:<?php echo esc_attr($btn_color);?>; } <?php
    }
}
add_action('wp_head','my_inline_css');

However i don’t know where that $btn_color value is set. You might want to add this information to your question to be able to get an accurate answer.