First order differential qusetion [ ]

In summary, a first order differential equation is a type of mathematical equation that describes the relationship between a variable and its rate of change over time. It is typically in the form of dy/dx = f(x) and is easier to solve than higher order differential equations. Applications of first order differential equations include modeling population growth and predicting the spread of diseases. These equations can be solved using various methods, but not all of them can be solved analytically. Some may require numerical methods or have no solution at all.
  • #1
thomas49th
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0
First order differential qusetion [urgent]

Homework Statement


Question 7
HL2001.jpg



Homework Equations





The Attempt at a Solution


I can do part a)

and i can begin part b, using separation of variables I get:

1/4 ln |1+2v| = ln|x| + C

but how do i use this to solve equation I

Thanks :)
 
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  • #2


Once you get v(x)

just substitute the known relationship v = y/x
 

Related to First order differential qusetion [ ]

1. What is a first order differential equation?

A first order differential equation is a type of mathematical equation that describes the relationship between a variable and its rate of change over time. It is in the form of dy/dx = f(x), where y is the dependent variable, x is the independent variable, and f(x) is a function of x.

2. What is the difference between a first order differential equation and a higher order differential equation?

A first order differential equation only involves the first derivative of the dependent variable, while higher order differential equations involve multiple derivatives. First order differential equations are also typically easier to solve than higher order ones.

3. What are some applications of first order differential equations?

First order differential equations have many applications in science and engineering, including modeling population growth, predicting the spread of diseases, and understanding the behavior of electric circuits.

4. How do you solve a first order differential equation?

There are various methods for solving first order differential equations, including separation of variables, integrating factors, and using substitution. The specific method used depends on the form of the equation and the initial conditions given.

5. Can all first order differential equations be solved analytically?

No, not all first order differential equations can be solved analytically. Some equations may be too complex to solve using traditional methods, and numerical methods may be required to approximate a solution. Additionally, some equations may have no solution at all.

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