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The Laplace transform of the differential equation y" + ay' + by = f(t). Assume that y(0) = 5, y'(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectively
- a)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)
- b)s2Y(s) - 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)
- c)s2Y(s) - 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)
- d)s2Y(s) + 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The Laplace transform of thedifferentialequation y" + ay + by = f...
A second-order differential equation is represented as:
y" + ay' + by = f(t)
The Laplace transform of the above equation with the initial condition is:
s2Y(s) - sY(0) - Y'(0) + a[sY(s) - Y(0)] + bY(s) = F(s)
y" + ay' + by = f(t)
The Laplace transform of the above equation with the initial condition is:
s2Y(s) - sY(0) - Y'(0) + a[sY(s) - Y(0)] + bY(s) = F(s)
Calculation
Given, y(0) = 5, y'(0) = 10
S2Y(s) - 5s - 10 + a (sY(s) - 5) + bY(s) = F(s)
Hence, the correct answer is option 2.
Given, y(0) = 5, y'(0) = 10
S2Y(s) - 5s - 10 + a (sY(s) - 5) + bY(s) = F(s)
Hence, the correct answer is option 2.
Most Upvoted Answer
The Laplace transform of thedifferentialequation y" + ay + by = f...
Understanding the Differential Equation
The given differential equation is:
y'' + ay + by = f(t)
To solve it using the Laplace transform, we need to apply the transform to each term in the equation.
Applying Laplace Transforms
1. Transform of y'':
- The Laplace transform of y''(t) is s²Y(s) - sy(0) - y'(0).
2. Transform of y:
- The Laplace transform of y(t) is Y(s).
3. Transform of f(t):
- This is simply F(s).
Substituting Initial Conditions
Given initial conditions are:
- y(0) = 5
- y'(0) = 10
Plugging these values into the Laplace transform:
1. For y'':
- s²Y(s) - 5s - 10
2. For y:
- a(sY(s) - 5) (since y(0) = 5)
3. Combine Everything:
- The full equation becomes:
s²Y(s) - 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)
Final Formulation
From the steps above, we can simplify:
- The correct equation is:
s²Y(s) - 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)
This matches option b, confirming its correctness.
Conclusion
Therefore, the correct answer is option 'b', as it accurately reflects the application of the Laplace transform to the given differential equation with the specified initial conditions.
The given differential equation is:
y'' + ay + by = f(t)
To solve it using the Laplace transform, we need to apply the transform to each term in the equation.
Applying Laplace Transforms
1. Transform of y'':
- The Laplace transform of y''(t) is s²Y(s) - sy(0) - y'(0).
2. Transform of y:
- The Laplace transform of y(t) is Y(s).
3. Transform of f(t):
- This is simply F(s).
Substituting Initial Conditions
Given initial conditions are:
- y(0) = 5
- y'(0) = 10
Plugging these values into the Laplace transform:
1. For y'':
- s²Y(s) - 5s - 10
2. For y:
- a(sY(s) - 5) (since y(0) = 5)
3. Combine Everything:
- The full equation becomes:
s²Y(s) - 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)
Final Formulation
From the steps above, we can simplify:
- The correct equation is:
s²Y(s) - 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)
This matches option b, confirming its correctness.
Conclusion
Therefore, the correct answer is option 'b', as it accurately reflects the application of the Laplace transform to the given differential equation with the specified initial conditions.
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The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer?.
The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer?.
Solutions for The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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Here you can find the meaning of The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The Laplace transform of thedifferentialequation y" + ay + by = f(t). Assume thaty(0) = 5, y(0) = 10, Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectivelya)s2Y(s) + 10s + 5 + a(sY(s) + 10) + bY(s) = F(s)b)s2Y(s)- 5s - 10 + a(sY(s) - 5) + bY(s) = F(s)c)s2Y(s)- 10s - 5+ a(sY(s) - 10) + bY(s) = F(s)d)s2Y(s)+ 5s + 10+ a(sY(s) + 5) + bY(s) = F(s)Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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