Problem: Find the solution of the differenial equation that satisfies the given intial condition.
The intial condition: .
I rewrite it as:
By integrating both sides and using integration by parts for the right side, I obtained:
The problem here is that I can not solve the last equation for so that I can use the intial condition to find the particular solution.
What I know is: solve the equation for , then in the resulting function put and equate it to zero, and solve the resulting equation for the constant and substitute the value of the constant in the general solution to get the particular solution.
I did not understand why this means I should put .
please, anyone can explain it?