Find the Solution to the equation DyDt y25 t y4 when t1Sol

Solution

Find the Solution to the equation -

Dy/Dt= y^2(5 + t)

y=4 when t=1

dy/y^2 = (5+t)dt

take integrtaion

-1/y = 5t + t^2/2 +C

-1/4 = 5 + 1/2 + C

C = -23/4

-1/y = 5t + t^2/2 -23/4

y = -1 /(5t + t^2/2 -23/4)