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

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SUMMARY

The discussion centers on solving the first-order ordinary differential equation (ODE) given by the expression [x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0. The initial attempts at substitution, specifically using v = x^2 + y^2, were unsuccessful, as the equation is neither exact nor homogeneous. A suggested alternative is to use the substitution u = y/x, which transforms the equation and may allow for separation of variables. This approach is presented as a viable method to potentially solve the differential equation.

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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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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.
 

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