Question: Differential Equations Topic: Laplace Transform Prove each item carefully. Kindly write complete proofs. f4. L(cos 2x - 3x + e-3x) = S + 52 +

Differential Equations

Topic: Laplace Transform

Prove each item carefully. Kindly write complete proofs.

\f4. L(cos 2x - 3x + e-3x) = S + 52 + 4 S+3 5. L -5 sin (2x + ") = - 5(2+s) V2(s2+4) Hint: Use Sum and Difference of Two Angles Identities (Angles are in radians) 6. L-1(2+ 2 =202x X 127. C-1 1 S 1 + + s+ 2 $2+ 4 = e-2x + cos 2x + sin V3x 8. L-1 3 20 + 10x3 c I W $2+1 $4 = 3 sin x + 3 3 2/2\f

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