First Order Differential Equations where a<x<b (Intial value?)

In summary, the conversation is about trouble understanding what to do when a First order equation has an inequality at the end of it. The person has solved the differential equation with a constant and is questioning what to do with the inequality and if it is an initial value problem.
  • #1
kafuzz
1
0
Hi, I'm having trouble understanding what to do when a First order equation has an inequality at the end of it.

For example : sqrt(y-x^2y)*dy/dx = -xy where -1<x<1

I've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant.

What do I do with the inequality? Is it an initial value problem?
 
Physics news on Phys.org
  • #2
welcome to pf!

hi kafuzz! welcome to pf! :smile:
kafuzz said:
HI've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant.

your solution contains √(1 - x2) …

you'll probably find that if |x| > 1, you get a solution with √(x2 - 1), or maybe some inverse trig function :wink:
 

1. What is a first order differential equation?

A first order differential equation is a mathematical equation that describes the relationship between a function and its derivative. It involves only the first derivative of the function, and the goal is to find a function that satisfies the equation.

2. What does "a

In this context, "a

3. What is an initial value in first order differential equations?

An initial value is a known value of the function at a specific point within the given interval. It is used to determine the particular solution of the differential equation.

4. How do you find the particular solution of a first order differential equation?

To find the particular solution, you need to use the initial value to solve the differential equation. This can be done by using various methods such as separation of variables, substitution, or integrating factors.

5. What is the significance of first order differential equations in science?

First order differential equations are used to model various physical phenomena in science, such as population growth, radioactive decay, and fluid flow. They are also essential in solving complex mathematical problems and making predictions about real-life situations.

Similar threads

I Solving Differential Equation Using Reduction of Order
    • Differential Equations
Replies
2
Views
987
I How do I solve this first order second degree differential equation?
    • Differential Equations
Replies
7
Views
3K
I Fundamental matrix of a second order 2x2 system of ODEs
    • Differential Equations
Replies
2
Views
1K
General solution vs particular solution
    • Differential Equations
2
Replies
52
Views
814
I Expressing a differential equation into a different format
    • Differential Equations
Replies
1
Views
1K
I Integral-form change of variable in differential equation
    • Differential Equations
Replies
1
Views
1K
I Question about solving linear first order non-homogeneous ODEs
    • Differential Equations
Replies
3
Views
791
A Differential equation and Appell polynomials
    • Differential Equations
Replies
1
Views
1K
I On sub and super solutions: Teschl and others
    • Differential Equations
Replies
5
Views
653
I Runge-Kutta 4 w/ some sugar on the top: How to do error approximation?
    • Differential Equations
2
Replies
40
Views
537

Hot Threads

Recent Insights

Back
Top