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Q 4. (a) Show that if two functions f and g have the Laplace transforms F and G, respectively, then the Laplace transform of convolution f * g of two functions f and g is FG, that is, L(f * g) = L(f)L(g). (b) Using Laplace transform, solve the integral equation y + 2e^t ?[0 to t] y(?)e^(-?) d? = te^t. 

          Q 4. (a) Show that if two functions f and g have the Laplace transforms F and G, respectively, then the Laplace transform of convolution f * g of two functions f and g is FG, that is,

L(f * g) = L(f)L(g).

(b) Using Laplace transform, solve the integral equation

y + 2e^t ?[0 to t] y(?)e^(-?) d? = te^t.
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Q 4. (a) Show that if two functions f and g have the Laplace transforms F and G, respectively, then the Laplace transform of convolution f * g of two functions f and g is FG, that is, L(f * g) = L(f)L(g). (b) Using Laplace transform, solve the integral equation y + 2e^t ?[0 to t] y(?)e^(-?) d? = te^t.

Added by Jacob G.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Q 4. (a) Show that if two functions f and g have the Laplace transforms F and G, respectively, then the Laplace transform of convolution f * g of two functions f and g is FG, that is, L(f * g) = L(f)L(g). (b) Using Laplace transform, solve the integral equation y + 2e^t ∫[0 to t] y(τ)e^(-τ) dτ = te^t.
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Transcript

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00:01 Now we have l of f is given to us as f and l of g that is laplace is given to us as g.
00:09 Then to prove l of f convolution g is equal to l of f into l of g...
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