Here's why:
* Dying of Cancer: The movie features a woman named Allie Hamilton, who is diagnosed with a terminal illness (though not explicitly stated to be cancer).
* Writing a Book: While Allie is dealing with her illness, she dedicates her time to writing a book about her relationship with her husband, Noah Calhoun.
* Husband Trying to Find a Cure: While not the primary focus, Noah is depicted as desperately trying to find a way to cure Allie's illness.
However, it's important to note:
* The film's main plot revolves around the love story of Allie and Noah, and the illness is more of a tragic backdrop.
* The movie doesn't explicitly focus on Noah's search for a cure, but rather his unwavering love and support for Allie.
There might be other movies that fit your description more closely, but "The Notebook" is the most likely candidate based on your provided details.