Well when you make the substitution then that means , so substituting into your DE you get
This is now first order linear and so can be solved using an integrating factor.
Hi its me again and I have return with more question that I currently got stuck on
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For the following differential equation
,
show that the substitution , yields the differential equation for
Hence find the solution to the original differential equation that satisfies the condition . Find the interval on which the solution to the initial value problem is defined.
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So I first set out to integrate first, however I have a problem that I do not know how to move to the otherside of the equation
e.g.
what I did is
I integrated by using integration by parts with u=tan(x) and
so the equation become
+ C
I'm certain that my integration is wrong, since y(0)=2 will result in
The same problem also applies to
since I do not know how to move, the and to the other side of the equation. So can any body tell me how to integrate this question?
Thanks
Junks
P.S. I finally posted this in latex
edit: I'll try to use First Order, O.D.E but since will first order O,D,E work there?
By first order O.D. E
I found my to be
is this correct?
I have more question to ask in regards to this same question.
so I got
since then
I subbed this value of y into
the equation become
If I did not made any mistake in the process, how do you integrate this equation ?
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I think I need to integrate so i can solve for this
"Hence find the solution to the original differential equation that satisfies the condition . Find the interval on which the solution to the initial value problem is defined."
It should be du/dx = - tan x - sec x/2
not the du/dx = -u tanx - 2sec x given above.
you then take the onto the LHS and you now have a linear first order ODE.
integrating factor is sec x.
get down to u = -sinx/2 + C cos x
from y= sinx +1/u, u = 1/(y-sinx)
Im not sure where to go from here, can anyone help solving for y?
I guess we didnt have exactly the same question
Im not sure if what i did is right, but try sub u into y then y into dy/dx
P.s. writing on my phone right now so I couldnt write a latex