Free counters!

суббота, 12 июля 2014 г.

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