# Differential Equations Question

• MeMoses
In summary: This should give you four new equations with just x and y in them. You can then try to match these simpler equations to the original four.In summary, you are asked to match four given differential equations with four possible solutions. To solve this problem, you can find the first and second derivatives of the given solutions and substitute them into each of the differential equations. Then, try to match the resulting equations to the original four. This approach should help you solve the problem even if you haven't covered second order DEs yet.

## Homework Statement

Match each of the differential equations with a solution from the list below.
1. 2x^2 * y'' + 3xy' = y
2. y'' + 12y' + 36y = 0
3. y'' - 12y' + 36y = 0
4. y'' + y = 0

And then the possible solutions A-D

## The Attempt at a Solution

This is from a web assignment from a ODE course which just started. We have only cover first order linear, homogenous ODE's and vairable seperable. I have no idea where to start here. Am I just overlooking something? Do I need to work backwards from the solutions? Any help to get me started would be greatly appreciated.

MeMoses said:

## Homework Statement

Match each of the differential equations with a solution from the list below.
1. 2x^2 * y'' + 3xy' = y
2. y'' + 12y' + 36y = 0
3. y'' - 12y' + 36y = 0
4. y'' + y = 0

And then the possible solutions A-D

## The Attempt at a Solution

This is from a web assignment from a ODE course which just started. We have only cover first order linear, homogenous ODE's and vairable seperable. I have no idea where to start here. Am I just overlooking something? Do I need to work backwards from the solutions? Any help to get me started would be greatly appreciated.

If you haven't done anything with 2nd order DEs yet, probably the best course of action is find the 1st and 2nd derivatives of the solutions you are given, and substitute them into each of the four given differential equations.

## 1. What are differential equations?

Differential equations are mathematical equations that describe the relationships between a function and its derivatives. They are used to model various natural phenomena and physical processes.

## 2. What is the purpose of solving differential equations?

The purpose of solving differential equations is to find the unknown function that satisfies the given equation and its boundary conditions. This allows us to predict the behavior of a system over time and make informed decisions.

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

The different types of differential equations include ordinary differential equations, partial differential equations, and stochastic differential equations. They can also be classified by their order, linearity, and whether they are autonomous or non-autonomous.

## 4. What are some real-life applications of differential equations?

Differential equations have a wide range of applications in various fields such as physics, engineering, economics, biology, and chemistry. They are used to model the movement of objects, population growth, heat transfer, and electrical circuits, among others.

## 5. How can I solve a differential equation?

There are various methods for solving differential equations, including separation of variables, integrating factors, power series, and numerical methods. The appropriate method depends on the type and complexity of the equation. It is important to also check for solutions that cannot be obtained using these methods, such as using software or approximations.