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Tuesday, March 31, 2015

Separation of Variables, 28

Category: Differential Equations

"Published in Newark, California, USA"

Find the general solution for


Solution:

Consider the given equation above 


Express y' as dy/dx as follows



By separation of variables, transpose dx to the right side of the equation and y² to the left side of the equation as follows



Integrate on both sides of the equation, we have  









Therefore, the general solution is


where B = 2C

Monday, March 30, 2015

Separation of Variables, 27

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 xy, we have 




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

Sunday, March 29, 2015

Separation of Variables, 26

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 xy, we have




Integrate on both sides of the equation, we have






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



Saturday, March 28, 2015

Separation of Variables, 25

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 y3ex2, we have 





Integrate on both sides of the equation, we have  








Therefore, the general solution is  


where A = -2C