Recent content by simo1

I have this equation u0(x) = a0x2(1-x)2 for 0≤ x ≤ 1 = 0 for x>1 i have to investigate how will a solitary initial state such as the one above deform as time goes on. I know it will not deform if c is constant. when they say I must do this by a well-lnown method and produce video...

I solved the equation and I had x(t) = sinh-1(sinhx0ec(0)t) is it possible to draw the characteristic curve of this function

I have this equation ux(x,t) + c(x)ux(x,t) = 0 x>0 I want to obtain information on how the initial input uo(x)=u(x,o) would deform when the sound speed is not constant. c(x) is the sound speedi wanted to start this by finding a DE for the level curves x=X(t) so that i can solve in terms the...

Re: quotient rings and homorphic images yes by R it is real numbers. and everythin that I wrote is as it is on the texbook. are there options here on mathshelpboard that we can use to show real numbers, complex etc

am given that ϕ is a function from F(R) tp RxR defined by ϕ(f)=(f(0),f(1)) i proved that ϕ is a homomorphism from F(R) onto RxR. i showed that 1) ϕ(f) +ϕ(g)=ϕ(f+g) [for all f,g in F(R)] 2)ϕ(f)*ϕ(g)= ϕ(f*g) how do i show that ϕ is onto and define the kernal??(Wasntme)

Re: clarity on groups my apologies I meant G=S3

someone had a post on finite quotient groups. i understood that but how does one list elements of G/H if H is a subgroup of G. where: G=Z10 H={α,β,δ}

Say x is a solution of the DE x’=f(x) and f is a continuous derivative on its domain, if lim┬(t→͚inifinity⁡〖x(t)〗=p then p is equilibriumhow can I show that this is true

Re: solving for x there is a part that says I need a function that is a slotion of the IVP now I looked at t and it is uniquely defined for each x in this this sinx = t + sin(2) Now they saying a function say ϕ:ϕ(Ɵ)= sin(Ɵ) - sin(2) which is a solution of the IVP such that ϕ' (Ɵ) = cos(Ɵ)...

I do not think I understand fully the concept of determining whether a function is autonomous> may you please help me understnad eg I was given thsi function x' = x^3 x(1)=1 i said f(z)=z^3 where f'(z) = 3x^2 and the domain of f is in all R where the domain of f is also in all R hence f' is...

Re: solving for x are you saying the only way possible to solve this is by the arcsin

Re: solving for x it it x(0)=2

I was given an DE equa x'=sec(x) : x(0) I then solved it to sin(x)= t + c(c0nstant) but then I can't solve for x cause they say we shouldn't use arcsin. what can I do

solve the initial value problem: x'=x^3 x(1)=1 my work dx/x^3 =dt then I integrated wrt t and obtained x^(-2) = t + c(c0nstant) where then this is 1/x^2 =t+c 1/x = square root of (t+c) then x= 1/sqrt(t+c) now when i apply the Initial value problem i get c = 0 and that is incorrect. where am...

Re: cyclic subgroup thank you so much