This is the question:
For which $A,\varphi$ does the function $A\sin(x+\varphi)$ solve the differential equation $(y')^2+y^2=1$?
I'm new to differential equations and I have no idea what this is supposed to mean. How do I use the function $A\sin(x+\varphi)$ to solve the differential equation? I can not find any example in my textbook that looks anything like the problem I have to solve here. Thanks.