Question

Obtain the differential equation of family of straight lines with slope and y intercept equal

Answer 1

Answer:

Equation of line whose slope is equal to y intercept, is

y = cx + c = c(x + 1) ...(i)

⇒dydx=c⇒dydx=c ...(ii)

On putting the value of c from Eq. (i) in Eq. (ii),

we get dydx=yx+1dydx=yx+1

⇒(x+1)dydx−y=0⇒(x+1)dydx−y=0

Which is the required differential equation

Answer 2

Answer:

ydx-(x+1)dy = 0

Step-by-step explanation:

1. Use the equation for slope intercept equation (y=mx+b)
2. Based on the question. Alter the above equation into...
                          y=(dy/dx)x + (dy/dx)
3. Seperate the dy/dx on the equation
                          y= (x+1)(dy/dx)
4. Simplify the equation to get the answer
                          ydx = (x+1)dy
                          ydx - (x+1)dy = 0