How can I integrate x^3/y^2 to solve this differential equation?

In summary, to find the solution to the differential equation dy/dx = x^3/y^2 with the initial condition y(2) = 3, you can separate the equation into x^3dx - y^2dy = 0 and integrate both sides. Using the initial condition, you can determine the constant of integration and find the final solution.
  • #1
Pseudo Statistic
391
6
How can I find the solution to this differential equation: dy/dx = x^3/y^2 given y(2) = 3?
I'd just like a hint on how I can integrate x^3/y^2... because that's where I'm falling.
Thanks for any responses.
 
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  • #2
Can you not separate the equation and then integrate?
 
  • #3
When I seperate, do I get:
x^3dx - y^2dy = 0?
Or is this wrong?
I was asking to check..
Thanks.
 
  • #4
Pseudo Statistic said:
When I seperate, do I get:
x^3dx - y^2dy = 0?
Or is this wrong?
I was asking to check..
Thanks.

That's fine- although you might find it simpler yet to write the equation as
x3dx= y2dy

Now integrate both sides. You get a "constant of integration" when you do that. Remember that y(2)= 3 means that when x= 2, y= 3. That will help you determine what that constant must be.
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between an unknown function and its derivatives. It is used to model many real-world phenomena in fields such as physics, engineering, and economics.

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

An ordinary differential equation (ODE) involves only one independent variable, while a partial differential equation (PDE) involves multiple independent variables. ODEs are used to describe systems that change over time, while PDEs are used to describe systems that change in multiple dimensions.

3. What are some common methods for solving differential equations?

Some common methods for solving differential equations include separation of variables, substitution, and integrating factors. Numerical methods such as Euler's method and Runge-Kutta methods are also used to approximate solutions to differential equations.

4. What are initial value problems and boundary value problems in the context of differential equations?

Initial value problems involve finding a solution to a differential equation that satisfies given initial conditions, while boundary value problems involve finding a solution that satisfies given boundary conditions. Initial value problems are typically solved using analytical methods, while boundary value problems often require numerical techniques.

5. How are differential equations used in real-world applications?

Differential equations are used in many real-world applications, such as modeling the growth of populations, predicting the motion of objects in space, and analyzing economic systems. They are also used in engineering to design and optimize systems and in physics to describe the behavior of physical systems.

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