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