solve the seperable first order DE dy/dx= (y-1)/x with initial condition y(2)=5?

Question

i got y = 2x+1 as end answer can anyone verify this answer?

Answer 1

your answer is correct

working:


dy/dx = (y-1)/x
dy/(y-1) = dx/x
ln(y-1) = lnx + c {c=constant}
ln(y-1) = lnx +lnk =ln(xk)
{where lnk=c , k is yet another constant}
y-1 = xk hence y =kx + 1
now satisfying the given condition

5 = 2k + 1
k = 2

hence the given solution is

y = 2x + 1

Answer 2

dy / (y - 1) = dx / x
log (y - 1) = log x + log k
log (y - 1) = log (kx)
y - 1 = kx
5 - 1 = 2k
k = 2
y - 1 = 2x
y = 2x + 1 (which looks promising!!)

Answer 3

dy/dx= (y-1)/x
dy/(y-1)=dx/x
In(y-1)=Inx +C
In(y-1)=Inx+InC
In(y-1)=In(xC)
y-1=xC
applying the initial conditions
y(2)=5
5-1=2C
4=2C
C=2
y-1=2x
y=2x+1