Question

Solving Differential Equation by Separation of variables
Find the particular solution y=f(x) to the given differential equation with the initial condition f(1)=2

Answer 1

dx/dy=xy^3

Answer 2

dx/x=y^3 dy
(y^4)/4=ln x+c
y^4=4lnx+C
when x=1,y=2
2^4=4ln 1+C
16=0+C
C=16
y^4=4lnx+16
ory^4=ln x^4+16