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

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

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 

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 y³e^x2, we have 

Integrate on both sides of the equation, we have  

Therefore, the general solution is  

where A = -2C