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Monday, April 27, 2015

Separation of Variables - Arbitrary Constant, 13

Category: Differential Equations

"Published in Newark, California, USA"

Find the particular solution for


when θ = 0, r = a.

Solution:

Consider the given equation above  


By separation of variables, transfer r³ to the left side of the equation as follows  



Integrate on both sides of the equation, we have  









Substitute the values of r and θ in order to solve for C as follows




 

Therefore, the particular solution is  





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