Help Differential Equations types

In summary, the speaker is struggling with solving the last 4 differential equations from a packet given by their professor. They have an exam the next morning and are looking for guidance or hints on how to approach the equations. They list the types of equations that the problems could potentially be. It is mentioned that one of the equations may be exact, but the speaker is unsure.
  • #1
BrettJimison
81
5

Homework Statement


Good day all,

My professor gave my class a packet of about 40 differential equations.
I for the life of me cannot figure out how t solve these last 4!
I also have an exam tomorrow morning, and would like finish these last few.

I don't need them solved out, I would just like to know what kind they are a maybe a hint to get started on them!
NOTE: They WILL be one of the following types:

seperable
Bernoulli
Exact
Linear
Homogeneous

Homework Equations



1) (2x+1)dx+((x^(2)-y)/x)dy=0

2)(cos2y-sinx)dx+(-2tanxsin2y)dy=0

3)(x^(2)y+xy-y)dx+(x^(2)y-2x^(2))dy=0

4)dy/dx=(-3x^(2)y-y^(2))/(2x^(3)+3xy)[/B]

The Attempt at a Solution



I have tried all sorts of ways, some take a page plus. I can't tell of these have obvious solutions or if there is a trick. I am a little worn out after solving 35 of them.
Any help would be greatly appreciated!
Thanks!
 
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  • #2
I think the 3rd one is exact, but I computed the partial derivatives in my head, so double check before you take my word on it.Actually nvm I don't think it is.
 

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. Ordinary differential equations involve a single independent variable and are often used to model physical and biological systems. Partial differential equations involve multiple independent variables and are commonly used in fields such as fluid dynamics and quantum mechanics. Stochastic differential equations involve random variables and are often used in finance and economics.

How do I determine the order of a differential equation?

The order of a differential equation is determined by the highest derivative present in the equation. For example, if the equation contains a second derivative, it is a second-order differential equation. In general, the order of a differential equation is equal to the number of times the highest derivative appears in the equation.

What is the difference between an initial value problem and a boundary value problem?

An initial value problem involves finding a solution to a differential equation that satisfies certain conditions at a single point, typically the initial condition. A boundary value problem, on the other hand, involves finding a solution that satisfies conditions at multiple points, typically the boundary conditions. In other words, initial value problems have one condition while boundary value problems have multiple conditions.

How do I solve a differential equation?

There is no one-size-fits-all approach to solving a differential equation, as the method used depends on the type and order of the equation. Some common methods include separation of variables, integrating factors, and using series solutions. It is important to first identify the type and order of the equation before selecting an appropriate method for solving it.

How are differential equations used in real-world applications?

Differential equations are used extensively in various fields such as physics, engineering, economics, and biology to model and understand real-world phenomena. For example, they can be used to model the growth of a population, the spread of diseases, and the flow of electricity. They also play a crucial role in the development of mathematical models and simulations, which are essential tools in scientific research and decision-making processes.

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