Need help solving simple Differential problem (help)

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In summary, the conversation discusses solving a heat transfer problem involving a differential equation. The equation is given in two forms and the process of solving it is explained, including the use of an integrating factor. The conversation also mentions the integration constant and how it can be calculated by the initial condition.
  • #1
Hi,

I am working out a heat transfer problem but I've to solve the Differential equation in order to keep going on but it's been a long time since i did any Differential. your help will be appreciated.

the equation in heat transfer form is T^2+z*k*T=z(C1*x+C2)

or

d^2y/dx+z*k*dy/dx=z(C1*x+C2)

z & k are constants, the equation need to be solved in terms of y(x)
 
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  • #2
if you set f=dy/dx then it becomes [tex]df/dx+zkf=z(c_1x+c_2)[/tex]. You multiply by the integrating factor [tex]e^{zkx}[/tex] and get
[tex](f(x)e^{zkx})'=ze^{zkx}(c_1x+c_2)[/tex]

and by integrating both sides and solving for f(x) you ll get

[tex]f(x)=\frac{z\int c_1xe^{zkx}dx+ z\int c_2e^{zkx}dx+ c_3}{e^{zkx}}[/tex]. You just have to compute the integrals which seem easy and get f(x). You then find [tex]y(x)=\int f(x)dx[/tex]
 
  • #3
where did C3 come from ?? thanks for the help
 
  • #4
Jennifer_88 said:
where did C3 come from ?? thanks for the help
It is the integration constant. You can calculate by the initial condition for f(=dy/dx). You ll have another c4 constant from the integration of f to find y.
 
  • #5


Hi there,

Thank you for reaching out for help with your heat transfer problem. Differential equations can be challenging, but I am happy to assist you in solving this problem.

Firstly, it would be helpful to know the initial conditions or boundary conditions for the problem, as these will be necessary for solving the differential equation. Additionally, it would be useful to know the physical interpretation of the constants z and k in the heat transfer equation.

To solve this differential equation, we can use standard techniques such as separation of variables, integrating factors, or substitution methods. I would recommend starting by rearranging the equation in terms of y(x) and its derivatives, and then applying the chosen method to solve for y(x).

If you need further assistance, please provide more information and I would be happy to guide you through the problem step by step. Good luck!
 

1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It expresses how a change in the independent variable affects the dependent variable.

2. What is the difference between a linear and a non-linear differential equation?

A linear differential equation has a linear relationship between the function and its derivatives, while a non-linear differential equation has a non-linear relationship. This means that the dependent variable and its derivatives are not raised to any power other than 1 in a linear equation, whereas in a non-linear equation, they can be raised to any power.

3. How do I solve a simple differential equation?

To solve a simple differential equation, you need to follow a standard procedure to eliminate the derivative term and find the solution. This involves finding an integrating factor and then integrating the equation on both sides.

4. Can I use a computer program to solve a differential equation?

Yes, there are various computational tools and software programs available that can help you solve differential equations. These programs use numerical methods to approximate the solution of the equation.

5. Why are differential equations important?

Differential equations are important because they are used to model and understand many natural phenomena in fields such as physics, engineering, and economics. They also have practical applications in various industries, including medicine, finance, and computer science.

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