Separation of Variables, 45

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 √a² - x² as follows  

Integrate on both sides of the equation, we have

   

Therefore, the general solution is 

Separation of Variables, 44

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 √a² - x² as follows 

Integrate on both sides of the equation, we have  

Therefore, the general solution is

Separation of Variables, 43

Category: Differential Equations

"Published in Newark, California, USA"

Find the general solution for

Solution:

Consider the given equation above 

Expand the given equation, we have

Integrate on both sides of the equation, we have 

Since ln x and ln y cannot be integrated by simple integration, then we need to use the integration by parts as follows

Therefore, the general solution is