abcalphabeta

i keep getting stuck in some problems of physics because the differential equation of the form a dy/dx + by = c f(x) keeps cropping up. is there any general method to solve this differential equation? when f(x) is sinusoidal, we avoid it using j operators and get the solution but in my particular problem f(x) is exponential.

whoops i forgot to mention the function is from N to N. so the equation is satisfied for n>=2 from this i infer f is strict increasing and f(n+1)-f(n)>=n-3 and many more inequalities. but none leads to any sort of contradiction.

find all natural nos n auch that n(n+1)(n+2)(n+3) has exactly 3 prime divisors. seems to never hold true for 'sufficiently' large nos. many small n satisfy.

f(f(n-1))=f(n+1)-f(n) if a solution exists (which i somehow doubt but am unable to prove)