Take the Laplace transform of the following Initial value problem and solve for Y(s) L{y(t)}: %3D / - 4y-45y S(t) y(0) = 0, y(0) = 0 %3D where S is a perlodic function defined by S1, 0

Take the Laplace transform of the following Initial value problem and solve for Y(s) L{y(t)}:<br>%3D<br>/ - 4y-45y S(t)<br>y(0) = 0, y(0) = 0<br>%3D<br>where S is a perlodic function defined by<br>S1, 0<t<1<br>S(t) =<br>10, 1<t< 2'<br>and S(t +2) = S(t) for all t 2 0.<br>%3D<br>Hint: : Use the formula for the Laplace transform of a periodic function.<br>Y(s):<br>The graph of S(t) (a square wave function):<br>

Extracted text: Take the Laplace transform of the following Initial value problem and solve for Y(s) L{y(t)}: %3D / - 4y-45y S(t) y(0) = 0, y(0) = 0 %3D where S is a perlodic function defined by S1, 0<><1 s(t)="10,"><>< 2'="" and="" s(t="" +2)="S(t)" for="" all="" t="" 2="" 0.="" %3d="" hint:="" :="" use="" the="" formula="" for="" the="" laplace="" transform="" of="" a="" periodic="" function.="" y(s):="" the="" graph="" of="" s(t)="" (a="" square="" wave="">

Jun 05, 2022

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Take the Laplace transform of the following Initial value problem and solve for Y(s) L{y(t)}: %3D / - 4y-45y S(t) y(0) = 0, y(0) = 0 %3D where S is a perlodic function defined by S1, 0

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