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Saturday, July 12, 2014

Variable Separation, 14

Category: Differential Equations

"Published in Vacaville, California, USA"

Find the general solution for


Solution:

Consider the given equation above 


In order to separate dx and dy from other variables, divide both sides of the equation by x√1 + y² as follows 




Integrate both sides of the equation, we have





Take the inverse natural logarithm on both sides of the equation, we have 



 
Therefore, the general solution is