Solving nonlinear first order DE w/ fractional exponents

In summary, the conversation discusses a simple differential equation with the initial condition of t=0,y=0. The person tried using Bernoulli's method to solve it, but encountered issues with the method when there is no y^(1) with q. They then ask for suggestions to solve the equation, mentioning using a computer or trying Wolfram Alpha. They later realize that the solution given by Wolfram Alpha is too complex for their college class and plan to change the equation.
  • #1
hotwheelharry
8
0
Hello. I have simple DE

y' + p y^(1/2) = q
---------------
y'=dy/dt
p,q=constant

I am confused because I tried bernoulli's method to solve and I think I exploded the universe.
Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there is no y^(1) with q anyway.

Any other suggestions to solve?
 
Physics news on Phys.org
  • #2
hotwheelharry said:
Hello. I have simple DE

y' + p y^(1/2) = q
---------------
y'=dy/dt
p,q=constant

I am confused because I tried bernoulli's method to solve and I think I exploded the universe.
Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there is no y^(1) with q anyway.

Any other suggestions to solve?

Do you need an analytic answer or can you use a computer to show it's behaviour through a numeric scheme? Also did you try wolfram alpha?
 
  • #3
Haha, totally forgot about wolfram alpha. sooo good. Anyway the solution it gave me is way to complex for my college DEQ class. I should probably change my equation. Thanks anyways.
 
  • #4
Hello,

Solutionof the ODE in attachment :
 

Attachments

  • ODE LambertW.JPG
    ODE LambertW.JPG
    18.6 KB · Views: 474
  • #5



Hello, solving nonlinear first order differential equations with fractional exponents can be challenging, but there are a few methods that can be used to solve them. One method is to use the substitution u = y^(1/2), which can transform the equation into a linear form. Another method is to use the power series method, where the equation is expanded as a series and then solved for the coefficients. Additionally, you can also try using the Laplace transform or numerical methods such as Euler's method or Runge-Kutta method. As for Bernoulli's method, it may not always work for every type of nonlinear equation, so it's important to explore other options as well. I hope this helps and good luck with your problem!
 

1. What is a nonlinear first order differential equation?

A nonlinear first order differential equation is a mathematical equation that involves the derivatives of an unknown function with respect to one independent variable. It is called "nonlinear" because the function and its derivatives can have terms that are not simply linear combinations of the function and its derivatives.

2. What are fractional exponents in the context of differential equations?

Fractional exponents in differential equations refer to the power to which a variable or function is raised. In other words, it is the number in the numerator of a fraction that represents a certain root of the variable or function.

3. How do you solve a nonlinear first order differential equation with fractional exponents?

To solve a nonlinear first order differential equation with fractional exponents, you can use various methods such as separation of variables, substitution, or integrating factors. It is important to first identify the type of equation and then use the appropriate method to solve it.

4. What are some applications of solving nonlinear first order differential equations with fractional exponents?

Nonlinear first order differential equations with fractional exponents have various applications in physics, engineering, and economics. They are used to model complex systems and phenomena such as population growth, chemical reactions, and heat transfer.

5. What are some challenges in solving nonlinear first order differential equations with fractional exponents?

One of the main challenges in solving these types of equations is that there is no general method that can be applied to all cases. Each equation may require a different approach, and some may not have analytical solutions. Additionally, the presence of fractional exponents can make the equations more difficult to manipulate and solve.

Similar threads

Replies
2
Views
2K
  • Differential Equations
Replies
2
Views
917
  • Differential Equations
Replies
1
Views
1K
  • Differential Equations
Replies
16
Views
818
Replies
3
Views
740
Replies
4
Views
1K
Replies
7
Views
2K
  • Differential Equations
Replies
1
Views
1K
  • Differential Equations
Replies
4
Views
1K
  • Differential Equations
Replies
7
Views
2K
Back
Top