Consider the differential equation 2y" + ty' 2y = 14, y(0) = y'(0) = 0. In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1., THEOREM 7.4.1 Derivatives of Transforms If F(s) = {f(t)} and n = 1, 2, 3, . . . , then £{t^f(t)} = (-1)" "F(S), dsn to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = £{y(t)}. Solve the first-order DE for Y(s). Y(s) = Then find y(t) = £¯¹{Y(s)}. y(t) =
Consider the differential equation 2y" + ty' 2y = 14, y(0) = y'(0) = 0. In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1., THEOREM 7.4.1 Derivatives of Transforms If F(s) = {f(t)} and n = 1, 2, 3, . . . , then £{t^f(t)} = (-1)" "F(S), dsn to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = £{y(t)}. Solve the first-order DE for Y(s). Y(s) = Then find y(t) = £¯¹{Y(s)}. y(t) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Ordinary Differential equation
please type the final answer clearly so that I can see clearly thank you.
![Consider the differential equation
2y" + ty' - 2y = 14, y(0) = y'(0) = 0.
In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1.,
THEOREM 7.4.1 Derivatives of Transforms
If F(s) = £{f(t)} and n = 1, 2, 3,..., then
£{t^f(t)} = (-1)^_F(s),
dsn
to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = £{y(t)}.
Solve the first-order DE for Y(s).
Y(s) =
Then find y(t) = £¯¹{Y(s)}.
y(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe462800b-ac16-4590-bafb-82d68c005ec5%2F4199168a-b270-4d64-b0f4-8ab79320244c%2Fzte0de_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the differential equation
2y" + ty' - 2y = 14, y(0) = y'(0) = 0.
In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1.,
THEOREM 7.4.1 Derivatives of Transforms
If F(s) = £{f(t)} and n = 1, 2, 3,..., then
£{t^f(t)} = (-1)^_F(s),
dsn
to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = £{y(t)}.
Solve the first-order DE for Y(s).
Y(s) =
Then find y(t) = £¯¹{Y(s)}.
y(t) =
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