Finishing touches to obtain the particular solution of a differential equation

I have been following the workings in my textbook on autonomous equations and could follow everything except for one step: obtaining the particular solution for y.

The general solution is:

To satisfy the initial condition  

Despite having been working on this for a good deal of time, I simply am unable to comprehend how they eventually solved for y, giving: 

Could you explain to me how this was arrived at?

Student X

Beginning with the general solution cited, ie

we proceed to invert both sides concurrently :

Now, making use of the substitution

we therefore have

Thereafter, this simply reduces to

Hope this helps. Peace.

Best Regards,

Mr Koh