Cannot solve simple equation

Questions
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1

Hello,
I am trying to solve a relatively simple differential equation

DSolve[y''[x] - ay[x] == -b, y[x], x]

that I know has a solution (in my notation):
y = C1 exp(sqrt(a)*t) +C2 exp(-sqrt(a)*t) +b/a.
However, Mathematica does not give me that solution, instead i get an output with some internal integrals.
Apparently, it is not because i use the software wrongly, because when I input a different equation

DSolve[y''[x] + y[x] == x, y[x], x]

I get the satisfying answer:

{{y[x] -> x + C[1] Cos[x] + C[2] Sin[x]}}

Is it not possible for Mathematica to solve the first equation? Https://www.symbolab.com/ can solve it…

2

ay is a single symbol, and ay[x] represents the value of a single function called ay.

Try it with a space: a y[x] represents a times y[x].