## Friday, April 3, 2015

### Separation of Variables, 31

Category: Differential Equations

"Published in Vacaville, California, USA"

Find the general solution for

Solution:

Consider the given equation above

Perform the algebraic operations and group according to their variables as follows

By separation of variables, transpose (1 - b cos θ) 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

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

Therefore, the general solution is

## Thursday, April 2, 2015

### Separation of Variables, 30

Category: Differential Equations

"Published in Vacaville, California, USA"

Find the general solution for

Solution:

Consider the given equation above

By separation of variables, transpose y to the right side of the equation and (4 + e2x) to the left side of the equation as follows

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

where E = C²

## Wednesday, April 1, 2015

### Separation of Variables, 29

Category: Differential Equations

"Published in Vacaville, California, USA"

Find the general solution for

Solution:

Consider the given equation above

By separation of variables, transpose dP to the right side of the equation and V to the left side of the equation as follows

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