6. Consider the differential equation y" (t) – 4y' (t) + 3y(t) = 5e2t. = .. (*) which we will solve by different methods

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6 Consider The Differential Equation Y T 4y T 3y T 5e2t Which We Will Solve By Different Methods 1 (57.37 KiB) Viewed 18 times

6. Consider the differential equation y" (t) – 4y' (t) + 3y(t) = 5e2t. = .. (*) which we will solve by different methods: (a) First find the general real solution of the associated homogeneous differential equation. (b) Find a particular solution of (*) using variation of parameters. (c) We will now find a particular solution of (*) by converting to a system of linear first-order differential equations and using diagonalization: Let y(t) = x1(t). Then y' (t) = x1(t). Put y' (t) = x2(t). X2 Then y" (t) = x'j(t) = -3x7(t) + 4xy(t) + 5e2t. 1 0 Now solve the system -3 4 using diagonalization. = = = 1 = = 0 ()-("s ()+(59 1 = 21 22 22 5e2t