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The number of arbitrary constants in the solution of a differential equation of degree 2 and order 3 is
- a)2
- b)3
- c)23
- d)1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The number of arbitrary constants in the solution of a differential eq...
Since, the number of arbitrary constants in a solution of a differential equation of order n is equal to its order.
So, number of arbitrary constants = Order of differential equation = 3
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The number of arbitrary constants in the solution of a differential eq...
Explanation:
Differential Equation of Degree 2 and Order 3:
- A differential equation of degree 2 and order 3 can be represented as a polynomial equation of the form:
\[ a_2 \frac{d^2y}{dx^2} + a_1 \frac{dy}{dx} + a_0 y = f(x) \]
where \( a_2 \neq 0 \) and \( f(x) \) is a function of \( x \).
General Solution:
- The general solution of a differential equation of degree 2 and order 3 will contain 3 arbitrary constants.
- These constants arise from the integration of the equation and reflect the flexibility in the solutions.
Number of Arbitrary Constants:
- The number of arbitrary constants in the solution of a differential equation is equal to the order of the equation.
- In this case, since the order of the differential equation is 3, the number of arbitrary constants in the solution will be 3.
Therefore, the correct answer is option B) 3.
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The number of arbitrary constants in the solution of a differential equation of degree 2 and order 3 isa)2b)3c)23d)1Correct answer is option 'B'. Can you explain this answer?
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