Question

solve this differential equation
d2y/dx2 + 4dy/dx +4y=epow(-x)* sin (pi/3 -x)
y(0)=y'(0)=0

Answer 1

*

Answer 2

\[\frac{ d ^{2}y }{ dx ^{2} }+4\frac{ dy }{ dx }+4y =e ^{-x}\sin (\frac{ \pi }{ 3 }-x)\]Is this the equation given?

Answer 3

Try (e^-x)(Asin(x) + Bcos(x)) for yp...

Answer 4

@sakshi1909 do you know what the first step is?

Answer 5

First the equation can be written as\[ay \prime \prime +by \prime +cy =G(X)\]Do you understand? Have you seen this before?

Answer 6

what class do you think he or she is in @calculusfunctions ?

Answer 7

@sakshi1909 I don't have a lot of time. I have to go soon so could please answer me. I'm trying to teach you but I can't be having a one way conversation with me, myself, and I.

Answer 8

@Algebraic! if he's asking this question then he should have clearly had at least a lesson on second-order homogeneous linear differential equations.

Answer 9

so why ask if he or she has ever seen a differential equation?

Answer 10

Sorry, I meant nonhomogeneous.

Answer 11

there's two pitfalls to a problem like this, why don't you just go over those...

Answer 12

@Algebraic! the reason I always ask them if they have learned something is because sometimes on these sites, people post questions which are beyond their level. They simply want learn the advanced stuff before mastering the Fundamentals. I know this because people have actually messaged me saying: "Sir I'm not at this level yet. I just wanted to learn for fun, or out of curiosity..." This is why I ask. I hope that answers your question.

Answer 13

Since he's clearly not responding, I have to go. I don't have time right now. If he returns you can continue with the lesson or I will explain the "pitfalls" as you say, when I return and if requested. However I really do have to go for now. Bye!