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(9 polnts) Consider the initial value problem if 0

(9 polnts) Consider the initial value problem if 0

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Consider the initial value problem 

(9 points) Consider the initial value problem * if0 <t<1 if 1<t<5 if 5 <t< 00, y+4y= 10 y(0) = 2. 0. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) = L {y(t)} = %3D c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = 0日 N W Delete 择+ F12 PrtSc Insert F7 F8 F9 F10 F11 F5 F6 小
Transcribed Image Text:(9 points) Consider the initial value problem * if0 <t<1 if 1<t<5 if 5 <t< 00, y+4y= 10 y(0) = 2. 0. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) = L {y(t)} = %3D c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = 0日 N W Delete 择+ F12 PrtSc Insert F7 F8 F9 F10 F11 F5 F6 小
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