Abu Dhabi University

College of Arts & Sciences,

Department of Applied Science and

Mathematics

MTT 205 Differential EquationsFall 2014, Final

Section: 01

ID Number:

Name:

1. Using Laplace transform find solution of the initial

value problem (IV P )

y′′ + 4y = sin 3x, y(0) = 0, y′(0) = 0

2. Find infinite power series solution of the differential

equation

(x2− 4)y′′ + 3xy′ + y = 0

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3. Find general solution of the system of differential equa-

tions

dx1

dt= 4x1 − 3x2

dx2

dt= 3x1 + 4x2

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4. Solve initial value problem

y′′ − 3y′ + 2y = 3e−x− 10 cos 3x

y(0) = 1, y′(0) = 2

Hint: Use undetermined coefficients method for finding a

yp particular solution.

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5. Find general solution of the differential equation

y′′ + 9y = 2 sec 3x

Hint: Use variation of parameter for finding a yp partic-

ular solution.

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6. Solve initial value problem and show that solutions

are linearly independent

y′′′ + 3y′′ − 10y′ = 0

y(0) = 7, y′(0) = 0, y′′(0) = 70

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7. Find solution of the differential equation

(3x2y3 + y4)dx + (3x3y2 + y4 + 4xy3)dy = 0

Hint: Use exact equation properties.

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8. Solve differential equation

xyy′ = x2 + 3y2

Hint: y′ = dydx

, and try to arrange in the form of

Bernoulli equation then solve.

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