## Monday, April 7, 2014

### Finding Equation - Curve, 11

Category: Differential Equations, Integral Calculus, Analytic Geometry, Algebra

"Published in Newark, California, USA"

Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with the slope of 5/2.

Solution:

The concavity of a curve is equal to the second derivative of a curve with respect to x. In this case, y" = d²y/ dx². Let's consider the given concavity of a curve

We can rewrite the above equation as follows

Multiply both sides of the equation by dx, we have

Integrate on both sides of the equation, we have

In order to get the value of arbitrary constant, substitute the value of the given point which is (1, 2) and the value of the given slope which is dy/dx = 5/2 to the above equation, we have

Hence, the above equation becomes

Multiply both sides of the equation by dx, we have

Integrate on both sides of the equation, we have

In order to get the value of arbitrary constant, substitute the value of the given point which is (1, 2) to the above equation, we have

Therefore, the equation of a curve is