Question:

If \(\frac{d}{dx}(2\frac{d^2y}{dx^2})^3= 7\), then the sum of order and degree of the differential equation is:

Updated On: Apr 19, 2024

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The Correct Option is D

The correct option is(D):4

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Let \( y = y(x) \) be the solution of the differential equation \[ \left( xy - 5x^2 \sqrt{1 + x^2} \right) dx + (1 + x^2) dy = 0, \quad y(0) = 0. \] Then \( y(\sqrt{3}) \) is equal to:
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If \( y = y(x) \) is the solution of the differential equation, \[ \sqrt{4 - x^2} \frac{dy}{dx} = \left( \left( \sin^{-1} \left( \frac{x}{2} \right) \right)^2 - y \right) \sin^{-1} \left( \frac{x}{2} \right), \] where \( -2 \leq x \leq 2 \), and \( y(2) = \frac{\pi^2 - 8}{4} \), then \( y^2(0) \) is equal to:
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Let a curve \( y = f(x) \) pass through the points \( (0,5) \) and \( (\log 2, k) \). If the curve satisfies the differential equation: \[ 2(3+y)e^{2x}dx - (7+e^{2x})dy = 0, \] then \( k \) is equal to:
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Let \( x = x(y) \) be the solution of the differential equation: \[ y = \left( x - y \frac{dx}{dy} \right) \sin\left( \frac{x}{y} \right), \, y > 0 \, \text{and} \, x(1) = \frac{\pi}{2}. \] Then \( \cos(x(2)) \) is equal to:
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Let for some function \( y = f(x) \), \(\int_0^x t f(t) \, dt = x^2 f(x), x>0\) and \( f(2) = 3 \). Then \( f(6) \) is equal to:
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A	Megaliths	(I)	Decipherment of Brahmi and Kharoshti
B	James Princep	(II)	Emerged in first millennium BCE
C	Piyadassi	(III)	Means pleasant to behold
D	Epigraphy	(IV)	Study of inscriptions