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fan_103
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1.Solve this differential equation
2.(x^2+y^2)y'=xy
3. Thanks
2.(x^2+y^2)y'=xy
3. Thanks
You don't have a "dx" on the rightfan_103 said:Ok mate I have tried it
(x^2+y^2)dy/dx=xy
Divide by [tex]y*(x^2+y^2)[/tex] : 1/y dy/dx= [tex]x/(x^2+y^2)[/tex].
[tex]\int {1/y}[/tex] dy= 1/2[tex] \int {x/(x^2+y^2)}[/tex]
That may seem like a technical point but it would have reminded you that you are integrating on the right with respect to x and y is some (unknown) function of x, not a constant. This is NOT a separable equation- that is you cannot get only x on one side of the equation and only y on the other.My answer is y=A [tex]\sqrt{x^2+y^2} [/tex].
fan_103 said:I forgot to write the dx on the right.
Thanks a lot mate!Really appreciate ur effort!
Why was this posted under "Precalculus"? Where should I post these kind of questions...
A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses how a quantity changes over time or space, and is used to model many natural phenomena in science and engineering.
There are various methods for solving differential equations, depending on the type and complexity of the equation. Common methods include separation of variables, integrating factors, and using power series or Laplace transforms.
The purpose of solving a differential equation is to find the unknown function that satisfies the equation, and to understand the behavior and relationships of the variables involved. This is important in many scientific fields, such as physics, engineering, and economics.
No, not all differential equations have closed-form solutions that can be expressed in terms of elementary functions. Some equations can only be solved numerically, while others may not have a solution at all.
Yes, some tips for solving differential equations include: understanding the type of equation and choosing an appropriate method, breaking down the equation into smaller parts, and checking the solution for correctness. It is also helpful to have a good understanding of calculus and algebra.