Solve the Separable Differential Equation for u

In summary, a separable differential equation is a type of differential equation that can be solved by separating the dependent and independent variables on opposite sides of the equation and integrating each side separately. The steps involved in solving one include separating the variables, integrating, adding a constant of integration, and solving for the dependent variable. There are some special cases to consider when solving a separable differential equation. Applications of this type of equation can be found in various fields such as science, engineering, economics, and finance.
  • #1
jwj11
37
0

Homework Statement



Solve the separable differential equation for u

du/dt = e^(6u + 8t)

Use the following initial condition: u(0) = 13.

Homework Equations



Techniques for solving separable differential equations.

1. Group variable and respective dy,dx,dz, etc. together
2. Integrate both sides
3. Solve for C using given data point
4. Solve for dependent variable

The Attempt at a Solution



http://img177.imageshack.us/img177/7321/differentialequation.jp
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
It isn't incorrect. What makes you think otherwise?
 
  • #3
Hmm.. I guess I am inputting it wrong. This is part of a webwork assignment (an online submission assignment)
 

Related to Solve the Separable Differential Equation for u

1. What is a separable differential equation?

A separable differential equation is a type of differential equation where the dependent variable and independent variable can be separated on opposite sides of the equation. This allows for the equation to be solved by integrating each side separately.

2. How do you solve a separable differential equation?

To solve a separable differential equation, you first need to separate the variables on opposite sides of the equation. Then, you can integrate each side separately. This will result in a general solution that can be solved for the dependent variable.

3. What are the steps involved in solving a separable differential equation?

The steps for solving a separable differential equation are as follows:

  1. Separate the variables on opposite sides of the equation
  2. Integrate each side separately
  3. Add a constant of integration to the side that was integrated
  4. Solve for the dependent variable

4. Are there any special cases when solving a separable differential equation?

Yes, there are some special cases that may arise when solving a separable differential equation. These include equations that have a constant as a solution, equations that result in a logarithm, and equations that require trigonometric substitutions.

5. What are some real-world applications of separable differential equations?

Separable differential equations are used in various fields of science and engineering to model and solve real-world problems. Some examples include population growth, chemical reactions, and radioactive decay. They are also used in economics and finance to model growth and decay of investments.

Similar threads

Solution of a parametric differential equation
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Verify Green's Formula for a Simple DE
    • Calculus and Beyond Homework Help
Replies
1
Views
310
Solve the system of differential equations
    • Calculus and Beyond Homework Help
Replies
10
Views
1K
Integral using substitution x = -u
    • Calculus and Beyond Homework Help
Replies
12
Views
1K
Solving modified heat equation
    • Calculus and Beyond Homework Help
Replies
5
Views
308
Solving a Non-Homogeneous Linear Differential Equation
    • Calculus and Beyond Homework Help
Replies
12
Views
1K
Homogeneous Differential Equation
    • Calculus and Beyond Homework Help
Replies
7
Views
2K
Using separation of variables in solving partial differential equations
    • Calculus and Beyond Homework Help
Replies
1
Views
872
Solve the given second order differential equation
    • Calculus and Beyond Homework Help
Replies
14
Views
482
Solve the given differential equation
    • Calculus and Beyond Homework Help
Replies
4
Views
982

Hot Threads

Recent Insights

Back
Top