# How to start Differential equation

• delsoo
In summary, the OP is asking for help with a math problem involving finding a stationary point and implicitly differentiating an expression with respect to time. They have received a hint for the first part and are now asking for the full solution. They have also shared a link to an image of the problem for reference.
delsoo
Mod note: Thread moved from technical math section. The OP has already been notified that this is not a suitable start to a request for homework help.
can anyone teach me how to start it? i really have no idea.. PART A

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You don't need to solve that equation for the two problems
The first problem amounts to finding a stationary point while the second requires you to implicitly differentiate that expression with respect to time.

Just a hint for i), the staionary point may only exist in a certain limit.

can you show the full working for part i please? i'd been thinking of this question for the whole day yet still can't get the ans

Here

Edit: In the last step I just plugged the value of x (which had to be done via a limit since it was positive infinty) back into the original expression for the answer

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Note to self: I should really learn LaTeX

if i do this way then how should i proceed ? note: i want to find x first , then sub the value of x which i get into the eqaution 1... after arranging the terms, i would get ln 0 ... then i can't find the value of x ...

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At the last step, you need to realize that the only way for the left hand side to equal zero is when x tends to positive infinity.

## 1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives, which represent the rate of change of a function, and is commonly used to model physical phenomena in science and engineering.

## 2. How do I solve a differential equation?

Solving a differential equation involves finding the function that satisfies the equation. This can be done analytically by using mathematical methods such as separation of variables or integrating factors, or numerically through approximation methods like Euler's method or Runge-Kutta methods.

## 3. What are the different types of differential equations?

There are several types of differential equations, including ordinary differential equations, partial differential equations, and stochastic differential equations. These types differ based on the number of independent variables and the types of derivatives involved.

## 4. What applications use differential equations?

Differential equations have a wide range of applications in science and engineering, including physics, chemistry, biology, economics, and engineering. They are used to model systems with changing variables, such as population growth, chemical reactions, and electrical circuits.

## 5. How can I improve my skills in solving differential equations?

To improve your skills in solving differential equations, it is important to have a strong foundation in calculus and linear algebra. You can also practice solving different types of differential equations using various techniques and methods, and seek help from textbooks, online resources, or a tutor.

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