Substituting into the differential equation and simplifying, we can verify that it is identically satisfied.
A more simple approach is to consider
The substitution now is more direct, producing as expected
See the Proof In Explanation.
For the sake of brevity, we will use the notations
Diff.ing the given eqn., using the Chain Rule, we get,
Rediff.ing, using the Product Rule, we have,
Now, note the following results derived by the Chain Rule , and
the Usual Rules of Diffn. These will be substd. in
Dividing throught by