# Differential equation right hand function

## Homework Statement

The question specifies the auxiliary eqution given is (D^2 + D - 2) = (e^x)/(x)
the method of variation of parameter must be used to find the particular solution to the right hand function. then finally the general soultion should be stated.

## Homework Equations

variation of paremeters formula.
yp = -y1∫y2 * g(x)/ (w(y1 , y2))
+ y2∫y1 * g(x)/ (w(y1 , y2))

## The Attempt at a Solution

i had solved the complementary function and had gotten yc = c1e-x + c2e-2x. then after applying the formula for variation of parameters i had gotten e-x*lnx/3 - e-2x/3 * ∫e3x / x
i cannot obtain an integral for ∫e3x / x i dont think it can be done have tried various mathods eg by parts, there are no suitable substitutions is it that there is no integral for the expression? i.e. it cannot be integrated.

Last edited:

LCKurtz
Homework Helper
Gold Member

## Homework Statement

The question specifies the auxiliary eqution given is (D^2 + D - 2) = (e^x)/(x)
the method of variation of parameter must be used to find the particular solution to the right hand function. then finally the general soultion should be stated.

## Homework Equations

variation of paremeters formula.
yp = -y1∫y2 * g(x)/ (w(y11 , y2))
+ y2∫y1 * g(x)/ (w(y11 , y2))

## The Attempt at a Solution

i had solved the complementary function and had gotten yc = c1e-x + c2e-2x. then after applying the formula for variation of parameters i had gotten e-x*lnx/3 - e-2x/3 * ∫e3x / x
i cannot obtain an integral for ∫e3x / x i dont think it can be done have tried various mathods eg by parts, there are no suitable substitutions is it that there is no integral for the expression? i.e. it cannot be integrated.

I haven't worked through this problem, but you are correct that ##\frac {e^{3x}} x## does not have an elementary antiderivative.

Mark44
Mentor

## Homework Statement

The question specifies the auxiliary eqution given is (D^2 + D - 2) = (e^x)/(x)
the method of variation of parameter must be used to find the particular solution to the right hand function. then finally the general soultion should be stated.

## Homework Equations

variation of paremeters formula.
yp = -y1∫y2 * g(x)/ (w(y1 , y2))
+ y2∫y1 * g(x)/ (w(y1 , y2))

## The Attempt at a Solution

i had solved the complementary function and had gotten yc = c1e-x + c2e-2x.
You have a mistake. What you have as e-x should be e+x. The other one is fine.
then after applying the formula for variation of parameters i had gotten e-x*lnx/3 - e-2x/3 * ∫e3x / x
i cannot obtain an integral for ∫e3x / x i dont think it can be done have tried various mathods eg by parts, there are no suitable substitutions is it that there is no integral for the expression? i.e. it cannot be integrated.

You have a mistake. What you have as e-x should be e+x. The other one is fine.
yes it is as u say but the problem still remains the same the∫e3x/x would still have to be determined

Mark44
Mentor
Doubell said:
yes it is as u say but the problem still remains the same the∫e3x/x would still have to be determined
But if you have an incorrect function in your variation of parameters formula, you'll definitely get the wrong answer.

Also, "textspeak" (such as "u" for "you") isn't permitted here at PF.