The answer to your question is true. For example, U(x,t) is a function that depends on x and t. X and t are independent. Do you think is possible for a dependent function to have derivatives as functions?
The answer in wolfram alpha is written in a compact form using the substitution e^2x. If the left hand side of the equation is solved implicitly you should get a answer to that portion of their answer that will look similar to the equation that you started with