Slope of the curve at a particular point (x_{1}, y_{1}) can be figured out by finding out derivative of the curve at the specific point.
To find equation of curve from the given given slope, we have to use the concept of differential equation.
Step 1 :
Assume the given slope as dy/dx
Step 2 :
Collect the variables and respective dy and dx on same sides and then integrate.
Step 3 :
After finding the integration, we will get the equation of curve in terms of x, y and arbitrary constant C.
Step 4 :
To solve for C, we may use the information that the curve passes through the particular point given. Apply the point for x and y and solve for C.
Problem 1 :
Find the equation of the curve whose slope is
(y - 1)/(x^{2} + x)
and which passes through the point (1, 0).
Solution :
Given slope (dy/dx) = (y - 1)/(x^{2} + x)
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM