dydt7y5 and find the particular solution stisfying the initi

Solution

dy/dt= -7y^5
=>dy/y^5 = -7 dt

intigrating both sides we get

-1/(4y⁴)=-7t+C

from initial condition i.e. y(0)=4

-1/(4*4⁴)=C => C=-1/1024

hence the final solution will be

-1/(4y⁴) =-7t-1/1024

y⁴ =1/(28t + 1/256)

or y(t)=[1/(28t + 1/256)]^1/4