Question

Solve the initial value problem, = , y(1) = 1. You can leave your answer in implicit form.

Answer 1

Given differential equation Bet on the range 0 with given condition 9119=. from given diff. equn. we get ay" (y=kny dy+ ty5dt = 0 __ take M= ayn (3y=P) , N= dy5 :: comme - 4ytteren - Syut. -- we yet, th e y - Integrating factors uz e dy multiplying with equation 4 we get y (3y + 2) dy + 1 hy dit zo Now this is an enact differential equation, Thebe forme there existe a funetion fruity such that = N = ty - DD EESScanned with CamScanner

:- f = f m dig + g(t) = f (3y = f) dy + g(t) = 169 - 200 g gent 964) only - 2 yyy + gray og mun agras now of a = t hy g'(b). [companing with ] - gra) = 0 = 8'(4) --& Feonstant =] A :.we get flyrt) = get the e is the solution. giren y cij=1 tane 62-3 The solution is more This is the bequined solution, CS$canned with CamScanner