How to solve these differential equations?

Question

I am working on a heat exchanger and found these differential equations from a paper. I never had such equation as you can see even if it's a single order differential equation a term "dy" is always hanging at right side of the equation.

I am trying to solve them in matlab but due to dy, I am not able to put it into an equation.

Can anyone help me to simplify the equation or any help on how such type of equations can be solved in matlab?

These are the equations:

Answer 1

Look at Eqs (23) and (24). They specify the definitions of \\dot{m}_p and \\dot{m}_s so that when you plug them into Eqs (19) and (20) they lose the floating differentials.