Help to reduce solution of differential equation: dy/dx=(xy+y)/(x+xy)

Thread starter Queren Suriano
Start date Jun 17, 2019
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Differential Differential calculus Differential equation

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The differential equation dy/dx=(xy+y)/(x+xy) leads to the implicit solution ln(y) + y = ln(x) + x + C. To solve for y explicitly, the Lambert W-function is required. Alternatively, local solutions can be explored for specific cases. The discussion emphasizes the complexity of the equation and the necessity of advanced mathematical tools for a complete solution. Understanding the use of the Lambert W-function is crucial for solving this type of differential equation.

Jun 17, 2019

Queren Suriano

Homework Statement: I have found this solution but I would like to solve for "Y" to write its general solution.

ln(y) +y = ln(x) + x +C

Relevant Equations: ln(y) +y = ln(x) + x +C
y=?

ln(y) +y = ln(x) + x +C
y=?

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Jun 17, 2019

fresh_42

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You will need Lambert's W-function for it, or go for some local solutions.

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