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# MTH401 Differential Equations GDB Solution & Discussion Last Date:18-08-2014

Discussion Topic:

Under what conditions the solution of the first order ordinary differential equation exist?

Furthermore, without solving the following initial value problem determine the interval in which the solution is certain to exist.

Opening Date: August 13, 2014 at 12:01 AM

Closing Date:  August 18, 2014 at 11:59  PM

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### Replies to This Discussion

Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

koi idea to dy kr b lngy yrrr

plz help kr do koi tu

2nd question ka kia answer hy? kisi ko pata hy kia?

sanu pehla nhi araha ap dusra bol rahy kamal kerty hen pandy g...!

Find the general solution by using an integrating factor:
y' + ytant = sint
dy / dt + ytant = sint
dy / dt + P(t)y = f(t)
P(t) = tant
f(t) = sint
I(t) = ℮^[∫ P(t) dt]
I(t) = ℮^(∫ tant dt)
I(t) = ℮^(-ln|cost|)
I(t) = ℮^(ln|1 / cost|)
I(t) = 1 / cost
I(t)y = ∫ I(t)f(t) dt
y / cost = ∫ tant dt
y / cost = -ln|cost| + C
y / cost = C - ln|cost|
y = cost(C - ln|cost|)

Find the particular solution by solving for the constant:
When t = π, y = 0
-C = 0
C = 0
y = -costln|cost|

Existence and Uniqueness Theorem

Suppose that f(t,y)  and partial deriavative of f(t,y) are continuous on a closed rectangle R  of the ty -plane. If , then the IVP

y'=f(t,y) ,y(t0)=y0

has a unique solution y(t)  on some t-interval containing t0.

i hate this subject..

jab ans ata he na ho tu hate he karna ha

but i love this subject

nafrat ni karna es subject sy. fail hojaye ga meri tarah

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