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Sunday, December 29, 2013

Solving Equations - Homogeneous Functions, 2

Category: Differential Equations, Integral Calculus

"Published in Newark, California, USA"

Find the general solution for


Consider the given equation above

Did you notice that the given equation cannot be solved by separation of variables? The first term is a combination of x and y in the group and there's no way that we can separate x and y. 

This type of differential equation is a homogeneous function. Let's consider this procedure in solving the given equation as follows


so that

Substitute the values of y and dy to the given equation, we have

The resulting equation can now be separated by separation of variables as follows

Integrate on both sides of the equation, we have


Hence, the above equation becomes

Therefore, the general solution is