--- /dev/null
+coefficient(1): a
+
+integrate (y'') -> -y':
+ IC: +1
+integrate (-y') -> y
+invert (y) -> -y
+sin = y
+
+integrate (omega') -> -omega
+a * sin -> a_times_sin
+omega' = a_times_sin
+
+invert (-omega) -> omega
+multiply (omega, omega) -> omega²
+multiply (omega², -y) -> -omega²y
+y'' = -omega²y