Solve 1st Order ODE: x^2+y^2+2xy+y^2+(x^3/3)dy/dx=0

In summary, the conversation discusses a differential equation of the first order and the attempt to solve it using substitution. The person tried using x^2+y^2=v as a substitution, but it did not work and the equation is not exact or homogeneous. They believe it can still be solved using substitution, but they are struggling to find the correct one. They are asking for help in solving the equation.
  • #1
ngj
1
0
i have this differential equation of the first order
[x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0
i tried to solve it by substitution putting x^2+y^2=v ,but it doesn't work also it is not exact or homogeneus to solve it by these methods. I still believe it can be solved using substitution but i can't reach to the correct one
so please help me solving this diff. equation
 
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  • #2
ngj said:
i have this differential equation of the first order
[x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0
i tried to solve it by substitution putting x^2+y^2=v ,but it doesn't work also it is not exact or homogeneus to solve it by these methods. I still believe it can be solved using substitution but i can't reach to the correct one
so please help me solving this diff. equation
You might try u = y/x ==> y = ux, so y' = u + u'x.

I can't guarantee it will work, but it's worth a try if you can get the DE to separate.
 

Related to Solve 1st Order ODE: x^2+y^2+2xy+y^2+(x^3/3)dy/dx=0

What is a 1st order ODE?

A first order ordinary differential equation (ODE) is a mathematical equation that relates an unknown function (usually denoted as y) to its derivative with respect to an independent variable (usually denoted as x). It is called "first order" because it involves only the first derivative of the unknown function.

What is the purpose of solving a 1st order ODE?

The purpose of solving a first order ODE is to find the unknown function y that satisfies the given equation. This allows us to model and understand various physical, biological, and economic phenomena that can be described by differential equations.

What is the process of solving a 1st order ODE?

The process of solving a first order ODE involves separating the variables, integrating both sides, and solving for the unknown function y. In some cases, additional mathematical techniques such as substitution or variation of parameters may be needed.

How can the given equation x^2+y^2+2xy+y^2+(x^3/3)dy/dx=0 be solved?

This equation can be solved by first separating the variables and then integrating both sides. This will result in a general solution, which can be further simplified by using initial conditions or boundary conditions.

What is the importance of solving ODEs in scientific research?

Solving ODEs is crucial in scientific research as it allows us to model and understand various physical, biological, and economic phenomena. ODEs are used in many fields, including physics, engineering, chemistry, biology, economics, and more. Solving ODEs also helps in making predictions and designing experiments to test these predictions.

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