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A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need to
  • a)
    change the initial condition to –y(0) and the forcing function to 2x(t)
  • b)
    change the initial condition to 2y (0) and the forcing function to −x (t)
  • c)
    change the initial condition to j √2y (0) and the forcing function to j √2x (t) 

     
  • d)
    change the initial condition to -2y(0) and the forcing function to −2x (t)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A system described by a linear, constant coefficient, ordinary, first ...
So if we want −2y (t) as a solution both x(t) and y(0) has to be doubled and
multiplied by –ve sign
x(t) → -2x(t)
y(0) → -2x(0)
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Most Upvoted Answer
A system described by a linear, constant coefficient, ordinary, first ...
The exact solution for the system described by a linear, constant coefficient, ordinary, first order differential equation is given by:

y(t) = e^(at) * C

where a is the constant coefficient and C is the constant of integration.
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A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need toa)change the initial condition to –y(0) and the forcing function to 2x(t)b)change the initial condition to 2y (0) and the forcing function to −x (t)c)change the initial condition to j √2y (0) and the forcing function to j √2x (t)d)change the initial condition to -2y(0) and the forcing function to −2x (t)Correct answer is option 'D'. Can you explain this answer?
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A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need toa)change the initial condition to –y(0) and the forcing function to 2x(t)b)change the initial condition to 2y (0) and the forcing function to −x (t)c)change the initial condition to j √2y (0) and the forcing function to j √2x (t)d)change the initial condition to -2y(0) and the forcing function to −2x (t)Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need toa)change the initial condition to –y(0) and the forcing function to 2x(t)b)change the initial condition to 2y (0) and the forcing function to −x (t)c)change the initial condition to j √2y (0) and the forcing function to j √2x (t)d)change the initial condition to -2y(0) and the forcing function to −2x (t)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need toa)change the initial condition to –y(0) and the forcing function to 2x(t)b)change the initial condition to 2y (0) and the forcing function to −x (t)c)change the initial condition to j √2y (0) and the forcing function to j √2x (t)d)change the initial condition to -2y(0) and the forcing function to −2x (t)Correct answer is option 'D'. Can you explain this answer?.
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