The easy way to check your work is to plug your solution into the differential equation. If it works, then you have the right solution. If it doesn't work, then you don't.
Also, if this is a Math problem, it is better to use fractions.
Thanks for the help so far.
I have found some mistakes but still don't get Galactus's Answer.
The Integrating factor is e ^(1/5x)
Then i get Y = -3/5e^ (-3/10x) + Ce^(1/5x) this is before the condition to find C.
This must be wrong but don't see what i've done wrong.Can you advise ?