Separation of Variables - Arbitrary Constant, 6

Category: Differential Equations

"Published in Newark, California, USA"

Find the particular solution for

when t = 0; r = r₀.

Solution:

Consider the given equation above  

By separation of variables, transfer dt to the right side of the equation and r to the left side of the equation as follows

Integrate on both sides of the equation, we have  

Substitute the values of r and t 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

Separation of Variables, 47

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 y ln y as follows

Integrate on both sides of the equation, we have  

Therefore, the general solution is

Separation of Variables, 46

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√x² - a² as follows 

   

 
Integrate on both sides of the equation, we have 

Take secant on both sides of the equation, we have

Therefore, the general solution is