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L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = ((99/74)sin(6t))-((1/37)e^(-36t))+((260/37) cos(6t))

L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = ((99/74)sin(6t))-((1/37)e^(-36t))+((260/37) cos(6t))

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.3: Euler's Method
Problem 15E: Use Eulers method to approximate the indicated function value to 3 decimal places, using h=0.1....
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Results for this submission Entered (s^2) *Y(s)-7*s-8+36*Y(s) s/[(s^2)+36] (s/[(s+36)*[(s^2)+36]])+ [(8+7*s)/[(s^2)+36]] (99/74)*sin(6*t)-(1/37)*[e^(-36*t)]+ (260/37)*cos(6*t) 99 74 Answer Preview s²Y(s) — 7s− 8 + 36Y(s) sin(6t) S (s +36)(s² +36) S s² + 36 - 1 37 e -36t 8+7s s² + 36 260 37 cos(6t) Result correct correct correct incorrect Message This answer is equivalent to the one you just submitted.
Transcribed Image Text:Results for this submission Entered (s^2) *Y(s)-7*s-8+36*Y(s) s/[(s^2)+36] (s/[(s+36)*[(s^2)+36]])+ [(8+7*s)/[(s^2)+36]] (99/74)*sin(6*t)-(1/37)*[e^(-36*t)]+ (260/37)*cos(6*t) 99 74 Answer Preview s²Y(s) — 7s− 8 + 36Y(s) sin(6t) S (s +36)(s² +36) S s² + 36 - 1 37 e -36t 8+7s s² + 36 260 37 cos(6t) Result correct correct correct incorrect Message This answer is equivalent to the one you just submitted.
Consider the initial value problem y" + 36y= cos(6t), y(0) = 7, y'(0) = 8. 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). (s^2Y(s))-7s-8+36Y(s) = = b. Solve your equation for Y(s). Y(s) = L{y(t)} = = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) s/(s^2+36) (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) ((99/74)sin(6t))-((1/37)e^(-36t))+((260/37)cos(6t)) help (formulas)
Transcribed Image Text:Consider the initial value problem y" + 36y= cos(6t), y(0) = 7, y'(0) = 8. 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). (s^2Y(s))-7s-8+36Y(s) = = b. Solve your equation for Y(s). Y(s) = L{y(t)} = = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) s/(s^2+36) (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) ((99/74)sin(6t))-((1/37)e^(-36t))+((260/37)cos(6t)) help (formulas)
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