well, it's all about chain rule! looking at as a function of and each of and as functions of and

applying the chain rule we'll get: and now apply the chain rule again, but

this time for and to get: and finally:

plugging these three in the equation your problem has given us, will give you:

which obviously has the general solution which, in terms of becomes:

for the required specific function, first see that:

we'd like to have i.e.

we also have this condition that which gives us:

solving the system of equations (1) and (2) gives us and where is a constant.thus

by the specific solution is