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1 1 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim

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2 2 Exercise (1) Solve the following set of equations using MATLAB x 1 + 2x 2 + 3x 3 + 5x 4 = 21 – 2x 1 + 5x 2 + 7x 3 – 9x 4 = 18 5x 1 + 7x 2 + 2x 3 – 5x 4 = 25 – x 1 + 3x 2 – 7x 3 + 7x 4 = 30 Solution x 1 = – 8.9896, x 2 = 14.12.85, x 3 = – 5.4438, x 4 = 3.6128.

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3 3 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (2) Differentiation of the following functions: (a)S 1 = exp(x 8 ) (b) S 2 = 3x 3 exp(x 5 ) (c) S 3 = 5x 3 – 7x 2 + 3x + 6

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4 4 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (3) Use MATLAB’s symbolic commands to find the values of the following integrals: (a) (9/40) (b) (7/3*pi^3) (c) (d)7x 5 – 6x 4 + 11x 3 + 4x 2 + 8x + 9

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5 5 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (4) Obtain the general solution of the following first order differential equations: (a) ans =(5*t)/6 + C6/(36*exp(6*t)) - 5/36 (b) (c) ans =A*t*x^3 + C11 (d) ans =(a^2*x^3)/2 + C15

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6 6 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (5) Obtain the general solution of the following: Using MATLAB program, find (a)General solution. (b)x(t) when all the initial conditions are zero. (c)x(t) when x(0) = 1 and Dx(0) = 2.

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7 7 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (6) (a) Expand the following function F(s) into partial fractions using MATLAB. (b) Determine the inverse Laplace transform of F(s) :

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8 8 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (7) Find the Laplace transform of the following function using MATLAB. (a) (b) (c) (d)

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DIFFERENTIAL EQUATIONS Note: Differential equations are equations containing a derivative. They can be solved by integration to obtain a general solution.

DIFFERENTIAL EQUATIONS Note: Differential equations are equations containing a derivative. They can be solved by integration to obtain a general solution.

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