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Sunday, July 6, 2014

Variable Separation, 11

Category: Differential Equations

"Published in Newark, 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 y2(1 - x) as follows




Integrate both sides of the equation, we have









Therefore, the general solution is


You can also integrate the given equation by rewriting 1 - x as x - 1 as follows










Therefore, the general equation is

 

Saturday, July 5, 2014

Variable Separation, 10

Category: Differential Equations

"Published in Newark, 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 x2 as follows 




Integrate both sides of the equation, we have









 
Therefore, the general solution is

 

Friday, July 4, 2014

Variable Separation, 9

Category: Differential Equations

"Published in Newark, 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) tan y 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