Solving Initial Value & Differential Equations

In summary, the conversation is about finding solutions for two different initial value problems and a general solution for a differential equation. The person asking for help is confused and has not paid attention in class or purchased the textbook. They are also asking for someone to explain the steps slowly. The experts respond by asking if these topics have been covered in their course and suggesting that they refer to their course notes and textbook for guidance. The person responds defensively and asks for help before their deadline.
  • #1
slain4ever
63
0

Homework Statement



1. Find he solution of the initial value problem:
x^2 (dy)/(dx) = 4y y(1)=2



2. Find the general solution of the differential equation:
(dy)/(dx) - 2y = e^(5x)


The Attempt at a Solution



i'm completely confused by this, no idea where to start. If someone could work through these questions and explaining (slowly) what they are doing in every step i would be extremely grateful.
 
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  • #2


Which of these topics have you studied?

1. Separation of variables
2. Linear equations
3. Constant coefficient equations
4. Integrating factors
 
  • #3


slain4ever said:

Homework Statement



1. Find he solution of the initial value problem:
x^2 (dy)/(dx) = 4y y(1)=2



2. Find the general solution of the differential equation:
(dy)/(dx) - 2y = e^(5x)


The Attempt at a Solution



i'm completely confused by this, no idea where to start. If someone could work through these questions and explaining (slowly) what they are doing in every step i would be extremely grateful.


Are these homework questions in a course? Do your course notes say nothing at all about such problems? Does your textbook have no relevant material? (If you answer yes to both of these questions you should ask for your money back.)


RGV
 
  • #4


yes, yes but I didn't buy the textbook coz I'm a cheap *** and there are plenty of places people are willing to share knowledge on a subject for free, like this forum.

and kurtz I don't know the names of what the processes are called, he just teaches them without naming them.

are any of you going to help or just tell me to pay attention in class?
 
  • #5


sorry if I was a bit rude, it's just that these questions and the rest that I've already done are due in a few days
 
  • #6


A bit rude? You have pretty much guarenteed that no one will want to help you.
 

What is an initial value in a differential equation?

An initial value in a differential equation is a known value of the dependent variable (usually denoted as y) at a specific point in the independent variable (usually denoted as x). It is used to find the particular solution to the differential equation.

What is the difference between an ordinary differential equation and a partial differential equation?

An ordinary differential equation involves only one independent variable, such as x, while a partial differential equation involves multiple independent variables, such as x and y. Additionally, the derivatives in a partial differential equation can be taken with respect to any of the independent variables, while in an ordinary differential equation, the derivatives are only taken with respect to the single independent variable.

What is the process for solving an initial value differential equation?

The process for solving an initial value differential equation involves finding the general solution, which is a function that satisfies the differential equation, and then using the initial value to find the particular solution. This is typically done by using integration techniques and solving for any constants that may be present in the general solution.

What is the importance of initial value problems in differential equations?

Initial value problems are important in differential equations because they allow us to find a unique solution to the equation. Without initial values, there can be an infinite number of solutions that satisfy the differential equation. The initial value helps to narrow down the possible solutions and find the one that fits the given conditions.

How are differential equations used in real-world applications?

Differential equations are used in a wide range of fields, including physics, engineering, economics, and biology. They can be used to model and predict the behavior of systems in the real world, such as the growth of a population, the spread of diseases, or the motion of objects. They are also used in solving various problems in fields such as electrical circuits, fluid dynamics, and chemical reactions.

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