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Let y(t)
be a solution to the differential equation y′=y2+t
, then y(t)
is differentiable
(a) once but not twice
(b) twice but not 3 times
(c) 3 times but not 4 times
(d) infinitely many times?
be a solution to the differential equation y′=y2+t
, then y(t)
is differentiable
(a) once but not twice
(b) twice but not 3 times
(c) 3 times but not 4 times
(d) infinitely many times?
Most Upvoted Answer
Let y(t) be a solution to the differential equation y′=y2+t, then y(t)...
Analysis of the Differential Equation y′=y^2+t
Understanding the given differential equation and the properties of its solution y(t) will help us determine the differentiability of y(t).
Properties of the Differential Equation
- The given differential equation is y′=y^2+t.
- This is a first-order ordinary differential equation.
Differentiability of y(t)
- To determine the differentiability of y(t), we need to analyze the right-hand side of the differential equation y′=y^2+t.
- Since y(t) appears squared in the equation, it suggests that y(t) might not be differentiable multiple times.
- The term t on the right-hand side does not affect the differentiability of y(t) as it is a continuous function.
Potential Number of Differentiations
- The term y^2 in the differential equation indicates that y(t) may only be differentiable once.
- Therefore, the solution y(t) is differentiable once but not twice.
Conclusion
- Based on the analysis of the given differential equation y′=y^2+t, the solution y(t) is differentiable once but not twice. The squared term in the equation limits the differentiability of y(t) to only one differentiation.
Understanding the given differential equation and the properties of its solution y(t) will help us determine the differentiability of y(t).
Properties of the Differential Equation
- The given differential equation is y′=y^2+t.
- This is a first-order ordinary differential equation.
Differentiability of y(t)
- To determine the differentiability of y(t), we need to analyze the right-hand side of the differential equation y′=y^2+t.
- Since y(t) appears squared in the equation, it suggests that y(t) might not be differentiable multiple times.
- The term t on the right-hand side does not affect the differentiability of y(t) as it is a continuous function.
Potential Number of Differentiations
- The term y^2 in the differential equation indicates that y(t) may only be differentiable once.
- Therefore, the solution y(t) is differentiable once but not twice.
Conclusion
- Based on the analysis of the given differential equation y′=y^2+t, the solution y(t) is differentiable once but not twice. The squared term in the equation limits the differentiability of y(t) to only one differentiation.
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Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times?
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Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times?.
Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let y(t) be a solution to the differential equation y′=y2+t, then y(t) is differentiable(a) once but not twice(b) twice but not 3 times(c) 3 times but not 4 times(d) infinitely many times?.
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