How Do You Find the Equation of a Curve with a Given Slope and Point?

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In summary, the conversation discusses finding the equation of a curve passing through a given point with a specific slope at any point and the use of ODE to solve for the equation. The process involves integrating and substituting for a constant using the given conditions.
  • #1
chakras
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Homework Statement



Find the equation of the curve that passes through the point (1,3) and has a slope of y/x^2 at any point (x,y).

Homework Equations



Is there any general equation for the equation of the curve?


The Attempt at a Solution



the only problem in my homework I am stuck at, do you have to integrate y/x^2? I am quite confused as to how one could get the exact equation of this curve. any help would be appreciated
 
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  • #2
y' = y/x^2

ODE

solve and sub for constant using codition point (1,3) lies on y=f(x)
 
  • #3
payumooli said:
y' = y/x^2

ODE

solve and sub for constant using codition point (1,3) lies on y=f(x)
Excellent suggestion.

Of course, this is dy/dx= y/x^2 which can be written as ydy= dx/x^2. Integrate both sides.
 

FAQ: How Do You Find the Equation of a Curve with a Given Slope and Point?

What is an equation of a curve?

An equation of a curve is a mathematical expression that describes the relationship between the coordinates of points on a curve. It is typically written in the form of y = f(x), where y represents the output or dependent variable and x represents the input or independent variable.

How do I find the equation of a curve?

To find the equation of a curve, you will need to know the coordinates of at least two points on the curve. Then, you can use the slope formula or other methods such as using a graphing calculator or software to determine the equation.

What is the difference between linear and non-linear equations of a curve?

A linear equation of a curve has a constant rate of change, meaning the graph of the equation is a straight line. On the other hand, a non-linear equation of a curve does not have a constant rate of change and the graph will not be a straight line.

Can an equation of a curve have multiple solutions?

Yes, an equation of a curve can have multiple solutions. This means that there can be multiple combinations of input and output values that satisfy the equation and lie on the curve.

Can I use an equation of a curve to predict future values?

Yes, an equation of a curve can be used to make predictions about future values. However, the accuracy of the predictions will depend on the reliability and validity of the data used to create the equation.

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