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

AI Thread Summary
To solve the differential equation dy/dx = x^3/y^2 with the initial condition y(2) = 3, the equation can be separated into x^3dx = y^2dy. After separating, both sides can be integrated, resulting in an equation that includes a constant of integration. The initial condition y(2) = 3 will help determine the value of this constant. This approach simplifies the integration process and leads to the solution of the differential equation.
Pseudo Statistic
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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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Can you not separate the equation and then integrate?
 
When I seperate, do I get:
x^3dx - y^2dy = 0?
Or is this wrong?
I was asking to check..
Thanks.
 
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.
 

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