Higher order General Method problem

[shaiqbashir]

hi guys!

okz this is a question from Higher Order Differential Equations. We are solving it from General Method to find $$y_{p}$$.

$$y_{p}=\frac{secax}{D^{2}+a^{2}}$$

I solve it and reaches this point:

$$y_{p}=\frac{1}{D+a\iota} e^{a\iota x} \int secax.e^{-a\iota x} dx$$

Please tell me some way to deal with this Integral Term. How can i solve it to get the final answer. What should be the best way to solve it,

i shall be thankful to u for this act of kindness.

take carez!

 

[jpr0]

What is the range of x? Are you solving for some particular range or the whole x-axis?
If the integral has upper and lower limits then it looks easier, particularly if you're integrating from $$-\infty$$ to $$\infty$$.
By the way, is $$\iota$$ some parameter, or $$\iota^2=-1$$?

 

[shaiqbashir]

thanks for ur interest!

there are no limits in this question

the letter i is basically iota!

 

[jpr0]

In that case the integral is straightforward:

$$sec\left(ax\right)e^{-iax} &=& \frac{\cos\left(ax\right)-i\sin\left(ax\right)}{\cos(ax)} \\ &=& 1 - i\tan\left(ax\right)\,.$$

These are just standard integrals...

 

[jpr0]

thanks for ur interest!
the letter i is basically iota!

(By the way my last post is assuming [if I understood correctly from what you said], that $$\iota=i$$).

 

[shaiqbashir]

yeah that's true jpr0

thanks for ur help!