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Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable?
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Lety(t) be a solution to the differential equation y'= y²+1, then y(t)...
Analysis of the Differential Equation y'= y²+1
First, let's analyze the given differential equation y'= y²+1.
Differentiability of the Solution y(t)
To determine if the solution y(t) to the given differential equation is differentiable, we need to check if y(t) is continuous and has a derivative at all points in its domain.
- Continuity of y(t): Since the solution to a first-order differential equation is continuous on its domain, y(t) is continuous.
- Existence of Derivative of y(t): To check if y(t) has a derivative, we need to ensure that y(t) is Lipschitz continuous with respect to y. Since the right-hand side of the given differential equation, y²+1, is Lipschitz continuous with respect to y, the solution y(t) is differentiable.
Therefore, the solution y(t) to the differential equation y'= y²+1 is indeed differentiable.
First, let's analyze the given differential equation y'= y²+1.
Differentiability of the Solution y(t)
To determine if the solution y(t) to the given differential equation is differentiable, we need to check if y(t) is continuous and has a derivative at all points in its domain.
- Continuity of y(t): Since the solution to a first-order differential equation is continuous on its domain, y(t) is continuous.
- Existence of Derivative of y(t): To check if y(t) has a derivative, we need to ensure that y(t) is Lipschitz continuous with respect to y. Since the right-hand side of the given differential equation, y²+1, is Lipschitz continuous with respect to y, the solution y(t) is differentiable.
Therefore, the solution y(t) to the differential equation y'= y²+1 is indeed differentiable.
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Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable?
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Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable?.
Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lety(t) be a solution to the differential equation y'= y²+1, then y(t) is differentiable?.
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