There is an existence theorem for second order linear differential equations that goes as follows:
Consider the Initial Value Problem (IVP)
If the functions and are continuous on the open interval that contains the point then the IVP has exactly one solution throughout the interval .
To start, in our example. I would suggest dividing through by and seeing if you can use the Main Theorem from there. Think about it a little more, and if you're still stuck I'll detail a little further what I had in mind for this exercise.