MHB Solving x in DE: sin(x)=t+c, No arcsin

[simo1]

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

 

[Opalg]

Re: solving for x

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

(i) What is the initial condition? x(0) = ??

(ii) There may be some trickery in this question. The sec function is undefined (or "infinite") at some points, so the equation needs to be interpreted cautiously at any such point.

 

[simo1]

Re: solving for x

(i) What is the initial condition? x(0) = ??

(ii) There may be some trickery in this question. The sec function is undefined (or "infinite") at some points, so the equation needs to be interpreted cautiously at any such point.

it it x(0)=2

 

[Opalg]

Re: solving for x

it it x(0)=2

In that case I don't see any way of avoiding an inverse sin function.

 

[simo1]

Re: solving for x

In that case I don't see any way of avoiding an inverse sin function.

are you saying the only way possible to solve this is by the arcsin

 

[Opalg]

Re: solving for x

are you saying the only way possible to solve this is by the arcsin

You solution $\sin x = t +c$ is correct. You can find the constant from the initial condition. Then you can either leave the solution in that form, or you can write it as $x = \arcsin(t+c)$. There is no way of writing the arcsin function in terms of other functions.

 

[simo1]

Re: solving for x

You solution $\sin x = t +c$ is correct. You can find the constant from the initial condition. Then you can either leave the solution in that form, or you can write it as $x = \arcsin(t+c)$. There is no way of writing the arcsin function in terms of other functions.

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) with ϕ(2) = 0

may I get an explanation how one gets to this equation