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Thanks, I got it now. I was thinking that the transform of the product was the product of the transforms.

Homework Statement Laplace Transform of u(t-∏/2)et (u is unit step function) Homework Equations Laplace Transform Table (any) The Attempt at a Solution I tried using the Laplace transform for the unit step function and the exponential function. L{u(t-∏/2)} = e-(∏s)/2...

((D+I)2+I)2y=0 Basis for kernel: ((D+I)2+I)2: {excos(x), exsin(x), xexcos(x), xexsin(x)} yp= A(x)excos(x) + B(x)exsin(x) yH= c1excos(x) +c2exsin(x) y=yp+yH y= A(x)excos(x) + B(x)exsin(x) + c1excos(x) +c2exsin(x) Is this correct? I still think something is wrong because I'm...

This is how I think I should solve it from my notes: ((D+I)2+I)((D+I)2+I)y=0 Basis for kernel: ((D+I)2+I): {excos(x), exsin(x)} ((D+I)2+I): {excos(x), exsin(x)} yp= Aexcos(x) + Bexsin(x) yH= c1excos(x) +c2exsin(x) y=yp+yH y= Aexcos(x) + Bexsin(x) + c1excos(x) +c2exsin(x)...

Homework Statement By using the method of differential operators, solve y''+2y'+2y=2e-xsinx 1. Determine what is the annihilator of the inhomogeneous term. 2. Find a particular solution. 3. Write the general solution for the equation. Homework Equations xneaxsin(bx) --> annihilated by...

Can someone please help me with this? It is very important.

I think I am missing something. Do I actually have to compute the 9th derivative of the original function? Another attempt is attached.

I'm sorry, could you please elaborate further on how to find the derivatives? I have attached my attempt but I don't think it's correct because I'm getting 0 for both the 9th and 10th derivatives.

Please find my attempt at the solution attached

I'm a little confused. I believe the bottom would become 1+u2. I tried using the power series for 1/(1-x) (sum from n = 0 to infinity of x^n). This left me with the sum from n = 0 to infinity of (x-1)^(2n+1). I then wrote out the Taylor Polynomial until the 9th power because I wanted to...

Homework Statement Find the MacLaurin series expansion of f(x)=(x^3)/(x+2). Find also the higher derivative f(10)(0) Homework Equations The Attempt at a Solution I'm not sure how to approach this question. The derivative of f(x) becomes larger and larger and I'm not sure how to...

Homework Statement Find the Taylor series expansion of f(x) = (x-1)/(1+(x-1)^2) about x=1 and use this to compute f(9)(1) and f(10)(1) Homework Equations The sum from n=0 to infinity of f(k)(c)/(k!) (x-c)k The Attempt at a Solution I'm not sure how to approach this...