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Monday, April 6, 2015

Separation of Variables, 34

Category: Differential Equations

"Published in Newark, California, USA"

Find the general solution for


Solution:

Consider the given equation above  


Divide both sides of the equation by cos² y in order to separate dx and dy from other variables as follows  




Integrate on both sides of the equation, we have

    






Therefore, the general solution is


where F = 2C.


Sunday, April 5, 2015

Separation of Variables, 33

Category: Differential Equations

"Published in Newark, California, USA"

Find the general solution for


Solution:

Consider the given equation above 


Divide both sides of the equation by (x - 1) in order to separate dx and dy from other variables as follows 




Integrate on both sides of the equation, we have   










Therefore, the general solution is  


where A = 1/C. 

Saturday, April 4, 2015

Separation of Variables, 32

Category: Differential Equations

"Published in Vacaville, California, USA"

Find the general solution for


Solution:

Consider the given equation above   


Divide both sides of the equation by y(x + 2) in order to separate dx and dy from other variables as follows




Integrate on 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