# Simple Differential problem (help)

• Jennifer_88
In summary: You solved the equation with respect to T, and then you are done.In summary, the conversation discusses solving a heat transfer problem using a differential equation. The equation is separable and can be solved through integration. The boundary conditions and steps for solving the equation are also mentioned. However, the conversation ends with the person admitting a lack of knowledge in differential equations and requesting help.

#### Jennifer_88

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.

d/dx[(k+aT)dT/dx]=0

i need thins in terms of T(x)

my boundary conditions T(x=0)=To
T(x=L)=TL

my work

d/dx[(k+aT)dT/dx]=0
(k+aT)dT=C1dx

KT+(a/2)T^2=C1x+C2

rearranging

T^2+(2/a)*k*T=(2/a)*(C1x+C2)

lets call (2/a)=z

T^2+z*k*T=z*(C1x+C2)

i could not get further from here due to lack of my Deferential equation knowledge. I really need to learn this as I'm expecting to see a lot more of this later and i actually took differential long time ago. any help would be appreciated

Jennifer_88 said:
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.

d/dx[(k+aT)dT/dx]=0
Since the derivative, with respect to x, of the quantity in brackets is zero, then the stuff in brackets must be a constant.

I.e., (k + aT)dT/dx = C

This equation is separable, so put all the terms involving T and dT on one side, and all the terms involving x and dx on the other side, and integrate.
Jennifer_88 said:
i need thins in terms of T(x)

my boundary conditions T(x=0)=To
T(x=L)=TL

my work

d/dx[(k+aT)dT/dx]=0
(k+aT)dT=C1dx

KT+(a/2)T^2=C1x+C2

rearranging

T^2+(2/a)*k*T=(2/a)*(C1x+C2)
This equation is quadratic in T, so use the quadratic formula to solve for T.

Write the equation in standard form, as
T^2+(2k/a)*T - (2/a)(C1x+C2) = 0

Jennifer_88 said:
lets call (2/a)=z

T^2+z*k*T=z*(C1x+C2)

i could not get further from here due to lack of my Deferential equation knowledge. I really need to learn this as I'm expecting to see a lot more of this later and i actually took differential long time ago. any help would be appreciated
Where you got stumped doesn't have anything to do with differential equations - this is pretty much plain algebra.

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## 1. What is a simple differential problem?

A simple differential problem is a mathematical problem that involves finding an unknown function by solving a differential equation. Differential equations are equations that involve the rate of change of a function.

## 2. What are the types of differential problems?

The types of differential problems include ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve finding a function of one variable, while PDEs involve finding a function of multiple variables.

## 3. How do you solve a simple differential problem?

To solve a simple differential problem, you must first identify the type of differential equation and then use various techniques such as separation of variables, integrating factors, or substitution to find the solution to the equation. It is also important to apply any initial or boundary conditions given in the problem.

## 4. What are the applications of differential problems?

Differential problems have many real-world applications, such as in physics, engineering, economics, and biology. They can be used to model and predict the behavior of systems that involve rates of change, such as population growth, chemical reactions, and motion.

## 5. What are some common mistakes when solving differential problems?

Some common mistakes when solving differential problems include forgetting to apply initial or boundary conditions, making algebraic errors, and using incorrect techniques for the type of differential equation. It is important to carefully check all steps of the solution and make sure they are mathematically sound.