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1. Find the general solution of the differential equation by using the method of undetermined coeficients 2. Solve using the method of variation of parameters 1. Given the differential equation +y-see(er), cisa constant. Find the constant if the Wronskian, W1 Heuce, find the solution of the differential equation. 4. Find the Laplace transform of (a) f(t)="col (b) f(t)-fir (c) P8 (1-3) 5. Given the piecewise continuous function {& (a) Express the above function in terms of unit step functions. (b) Hence, find the Laplace transform of f 7(0)- 05*<2 2<x<4 124 6. Using Convolution theorem, determine 7. Using Laplace transform, solve the simultaneous differential equatione de dy d dy given that (0)1 and y(0)-0. & Using Laplace transform, solve the simultaneous differential equations dz dy dt given that 0) and (0)-1. -4-2H(-1).
1. Find the general solution of the differential equation - 4y= 4 sin(2x) - 3e² by using the method of undetermined coeficients.
2. Solve d'y dy +2 + 5y = e cosec (2x) da² dax using the method of variation of parameters.
3. 4. 5. Given the differential equation d²y +²y=sec² (cx), cis a constant. dx² Find the constant c if the Wronskian, W = 3. Hence, find the solution of the differential equation. Find the Laplace transform of (a) f(t)e2t cosh² t (b) f(t) = t sin 6t (c) t³8 (t) Given the piecewise continuous function f(t) = 1, 0, -4t 0 < x < 2, 2 ≤ x < 4, t24. (a) Express the above function in terms of unit step functions. (b) Hence, find the Laplace transform of f(t).
6. Using Convolution theorem, determine ²¹{²+1}}" s(s² + 1) 8. 7. Using Laplace transform, solve the simultaneous differential equations dx dy dt dt dy dt given that x(0) = 1 and y(0) = 0. = S = 4x + e¹8(t - 3), Using Laplace transform, solve the simultaneous differential equations da dt dy dt given that x(0) = 0 and y(0) = -1. - y = 1, - - 4x = 2H(t-1),