Find the particular solution of the differential equation that satisfies the initial condition

Given,

and to find the particular solution of differential equation at  .

so proceeding further , we get.

=>

so , the equation is linear in y

and is of the form

so the general solution is given as

where I.F (integrating factor ) = 

Given,

and to find the particular solution of differential equation at  .

so proceeding further , we get.

=>

so , the equation is linear in y

and is of the form

so the general solution is given as

where I.F (integrating factor ) = 

on comparing we get ,

so ,

so ,

=>

=>

=>

=>

=

so , now to find the particular soultion at , we have to do as follows

=> y(1) =

=>

=>

=>

so the particular solution is

=