Recent content by Magnetons

I'm applying this rule on my first partial integral.. Yes, I've addressed the mistakes that's why I'm trying to expalining what I'm doing in solution .

As we can see the non homogeneous part is in the form of e^(ax).V( x) in our case v is a polynomial 2x . In this case we change f(D) in the denominator to f(D+a) and then only operate it with polynomial and leave the e^ax.

is there is any rule that we can't integrate first ..

Mentor note: Moved from a technical math section, so missing the template. TL;DR Summary: I'm trying to solve the differential equations (D^2 -4D + 3 )y = 2xexp(3x) + 3exp(x)Cos2x On this page , I've solve particular integral by 2 ways, 1st is above the line in which ( see 7th equality from...

how should I solve this equation

No ## u_t = 0 ## doesn't mention in question i assume it .

something different ..

don't know it is how the question is given in the book

using the equation ##u(x,y)=f(x)g(y)##, first, I substitute the value of ##u_{xx}## and ##u_{yy}## in the given PDE. after that solve the ODEs but I can't understand about the ##u_{t}##.In my solution, I put ##u_{t}=0## because u is only the function of x and y. Is it the right approach, to me...

Lemma Let f be a bounded function on [a,b]. If P & Q are partitions of [a,b] and P ##\subseteq## Q , then L(f,P) ##\leq## L(f,Q) ##\leq## U(f,Q) ##\leq## U(f,P) . Question is "How can P have bigger upper darboux sum than Q while it is a subset of Q"

I can only smile😊

I think it is "True" because the hypothesis is true and the conclusion is False. :cry::cry:But in the answer sheet, the answer is " This is False. The hypothesis is true, but the conclusion is false:## -1^2=-1## , not1."

Got it:smile::check:

Firstly I converted the given equation to a quadratic equation which is ##z^2- (\sqrt3)z+1=0## I got two solutions: 1st sol ##z=\frac {(\sqrt3 + i)} {2}## 2nd sol ## z=\frac {(\sqrt3 -1)} {2}## Then I found modulus and argument for both solution . Modulus=1 Arguments are ##\frac...