Selected topics in differential and integral equations assignment 1

SELECTED TOPICS IN DIFFERENTIAL AND INTEGRAL EQUATIONS
ASSIGNMENT 1

Please be divided group into 4 and solve problems following the Table 1

4- GROUP

	Group		Number 4.
1	АЛИБЕКОВ ИЛЁС САЛОХИДДИНОВИЧ	Exs 9	Q8
2	БОЛБЕКОВ САЙФИДДИН НАСРИДДИН ЎҒЛИ	Exe 2	Q3
3	ДАВРОНОВА ГУЛХАЙЁ ИСЛОМ ҚИЗИ	Exe 8	Q4, Q5
4	АБДУВОХИДОВА(ЖУМАНОВА) МАВЛУДА ҒАЙБУЛЛА ҚИЗИ	Exs 3, Exe 11	Q1, Q2
5	КЕНЖАЕВА САНОБАР ИБРАГИМОВНА	Exe 5	Q3
6	МАМАТКУЛОВ АБДУМАЛИК УРАЛОВИЧ	Exe 6	Q1
7	РАВШАНОВ ЗОЙИР САЙФУЛЛАЕВИЧ	Exe7	Q3
8	САМАТОВ БАРҲАЁТ АНОРБОЙ ЎҒЛИ	Exe 8	Q4
9	ТОЖИБОЕВА ДИЛАФРЎЗ НУРИДДИН ҚИЗИ	Exe 1	Q1
10	ЎРОҚОВА ЮЛДУЗ СОБИР ҚИЗИ	Exe 10	Q2
11	ХОЛМАНОВА КЛАРА ЯНГИБОЙ ҚИЗИ	Exe 4	Q4
12	ЭСИРГАПОВ ИЛЁСЖОН БОБОҚАНТ ЎҒЛИ	Exe 9	Q1

Exercises 1: Classify each of the following integral equations as Fredholm or Volterra integral
equation, linear or nonlinear, and homogeneous or nonhomogeneous:
1. u(x)=1+<sub> 

 </sub> Volterra integral equation

_{ }nonliner

F(x)=1 – nonhomogeneous

Exercises 2: Classify the following integro-differential equations as Fredholm integrodifferential equation or Volterra integro-differential equation. Also determine whether the
equation is linear or nonlinear:

Exercise 2: Q3

u_{ }(x)=_{ }

u(0)=1, u′(0)=0

_{ } Volterra integro-differential equation

_{ }nonlinear

F(x)=_{ } – nonhomogeneous

Exercises 3: Convert given differential equation to a corresponding integral equation or
integro-differential equation.

Exercise 3: Q1

u′(x)= _{ } u(0)=1

Volterra integral equation

Exercises 4: Verify that the given function is a solution of the corresponding integral or
integro-differential equation:

Question 2 Solution:

Exercise 5: Convert each of the Volterra integral equations to an equivalent initial value
problem.

Q3:

Exercises 6: Derive an equivalent Volterra integral equation to each of the following initial
value problems of first and second order.


Exercises 7: Derive the equivalent Fredholm integral equation for each of the following
boundary value problems:
Exercises 8: Solve the following Fredholm integral equations by using the Adomian
decomposition method.

Question 4 Solution:

_{ }

…… …… …….. ………

_{ })

Answer:

Question 5:

Solution:

,

Answer:

Exercises 9: Solve the given Fredholm integral equations by using the modified
decomposition method

Exercises 10: Solve the following Fredholm integral equations by using the variational
iteration method

Question 2:

Exercises 11: Solve the following Fredholm integral equations by using the direct
computation method: