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The order and degree of the differential equation y2 = 4a(x − a), where ‘a’ is an arbitrary constant, are respectively
  • a)
    1,2
  • b)
    2,1
  • c)
    2,2
  • d)
    1,1
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The order and degree of the differential equation y2 = 4a(x − a)...
y2 = 4a(x − a) … . . (1)
Order = 1.
Differentiating, both sides, we get

Putting in (1), we get 
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Most Upvoted Answer
The order and degree of the differential equation y2 = 4a(x − a)...
The given differential equation is y^2 = 4a(x). To determine the order and degree of this differential equation, we need to rewrite it in a more standard form.

First, let's rewrite the equation as y = ±√(4a(x)).

Now, differentiate both sides of the equation with respect to x:

dy/dx = ±(1/2)(4a(x))^(-1/2)(4a)' = ±(1/2)(4a(x))^(-1/2)(4a)

dy/dx = ±2a/(√(4a(x)))

Since this is a first-order differential equation, the order is 1. The degree of the differential equation is determined by the highest power of the derivative that appears in the equation. In this case, the highest power of the derivative is 1, so the degree is also 1.

Therefore, the given differential equation y^2 = 4a(x) is a first-order and first-degree differential equation.
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The order and degree of the differential equation y2 = 4a(x − a), where ‘a’ is an arbitrary constant, are respectivelya)1,2b)2,1c)2,2d)1,1Correct answer is option 'A'. Can you explain this answer?
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