ODE problem: 3x^2 y dx + (x^3 + 2y)dy = 0

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In summary, an ODE (ordinary differential equation) problem is a mathematical equation that relates a function to its derivatives. The solution to such a problem involves finding an expression for the unknown function that satisfies the equation and any given initial conditions, using various methods such as separation of variables, substitution, or specific techniques for different types of ODEs. The order of an ODE problem is the highest derivative that appears in the equation, while the degree is the exponent of the highest derivative. There is no general solution to all ODE problems, as the method of solving depends on its type and specific characteristics. However, there are techniques and strategies that can be applied to solve a wide range of ODE problems.
  • #1
brad sue
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I have two ODE with which I cannot to slove;

3x2ydx+(x3+2y)dy=0

I tried to change of variable y=v*x, but I still cannot find a way to solve it.

the second is:

(exsin(y)-2ysin(x))dx+(excos(y)+2cos(x))dx=0

here I have no idea


thank you
B
 
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  • #2
They are exact diff equ. Have you not seen how to solve such ode's?
 
  • #3
Surely you know other techniques for solving ODE? This problem is tailor-made for one of them.
 

FAQ: ODE problem: 3x^2 y dx + (x^3 + 2y)dy = 0

What is an ODE problem?

An ODE (ordinary differential equation) problem is a mathematical equation that relates a function to its derivatives. It involves finding the unknown function that satisfies the equation and any given initial conditions.

How do you solve an ODE problem?

The solution to an ODE problem involves finding an expression for the unknown function that satisfies the equation and any given initial conditions. This can be done using various methods such as separation of variables, substitution, or using specific techniques for different types of ODEs.

What is the order of an ODE problem?

The order of an ODE problem is the highest derivative that appears in the equation. In this case, the order is 1 since the highest derivative is dy.

What is the degree of an ODE problem?

The degree of an ODE problem is the exponent of the highest derivative in the equation. In this case, the degree is 3 since the highest derivative is x^3.

Is there a general solution to an ODE problem?

There is no general solution to all ODE problems. The method of solving an ODE problem depends on its type and specific characteristics. However, there are some techniques and strategies that can be applied to solve a wide range of ODE problems.

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