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Differential Equations
Quiz 2
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Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is
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cos x
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sec x
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e
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e
Explanation
sec x
The solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
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y = tan x
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y – x = k(1 + xy)
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x = tan y
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tan (xy) = k
Explanation
y – x = k(1 + xy)
The integrating factor of the differential equation \(\frac{dy}{dx}\) + y = \(\frac{1+y}{x}\) is
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\(\frac{x}{e^x}\)
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\(\frac{e^x}{x}\)
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xe
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e
Explanation
\(\frac{e^x}{x}\)
y = ae+ be satisfies which of the following differential equation?
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\(\frac{dy}{dx}\) + my = 0
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\(\frac{dy}{dx}\) – my = 0
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\(\frac{d^2y}{dx^2}\) – m²y = 0
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\(\frac{d^2y}{dx^2}\) +m²y = 0
Explanation
\(\frac{d^2y}{dx^2}\) – m²y = 0
The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
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\(\frac{sin x}{sin y}\) = c
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sin x sin y = c
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sin x + sin y = z
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cos x cos y = c
Explanation
sin x sin y = c
The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is
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(x² – y²)\(\frac{dy}{dx}\) = 2xy
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2 (x² + y²)\(\frac{dy}{dx}\) = xy
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2(x² – y²)\(\frac{dy}{dx}\) = xy
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(x² + y²) \(\frac{dy}{dx}\) = 2xy
Explanation
(x² – y²)\(\frac{dy}{dx}\) = 2xy
Family y = Ax + A³ of curves will correspond to a differential equation of order
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3
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2
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1
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not finite
Explanation
2
The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is
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an ellipse
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parabola
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circle
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rectangular hyperbola
Explanation
rectangular hyperbola
The general solution of the differential equation \(\frac{dy}{dx}\) = e
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y = ce
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y = ce
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y = (x + c)e
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y = (c – x)e
Explanation
y = (x + c)e
The solution of the equation (2y – 1) dx-(2x + 3)dy = 0 is
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\(\frac{2x-1}{2y+3}\) = k
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\(\frac{2y+1}{2x-3}\) = k
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\(\frac{2x+3}{2y-1}\) = k
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\(\frac{2x-1}{2y-1}\) = k
Explanation
\(\frac{2x+3}{2y-1}\) = k
The differential equation for which y = a cos x + b sin x is a solution is
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\(\frac{d^2y}{dx^2}\) + y = 0
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\(\frac{d^2y}{dx^2}\) – y = 0
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\(\frac{d^2y}{dx^2}\) + (a + b)y = 0
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\(\frac{d^2y}{dx^2}\) + (a – b)y = 0
Explanation
\(\frac{d^2y}{dx^2}\) + y = 0
The order and degree of the differential equation(\(\frac{d^2y}{dx^3}\))² – 3\(\frac{d^2y}{dx^2}\) +2(\(\frac{dy}{dx}\))= y are
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1, 4
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3, 4
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2, 4
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3, 2
Explanation
3, 2
The order and degree of the differential equation [1 + (\(\frac{dy}{dx}\))²] = \(\frac{d^2y}{dx^2}\) are
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1, \(\frac{3}{2}\)
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2, 3
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2, 1
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3, 4
Explanation
2, 1
The differential equation of the family of curves y² = 4a (x + a) is
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y² = 4\(\frac{dy}{dx}\) (x + \(\frac{dy}{dx}\))
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2y\(\frac{dy}{dx}\) = 4a
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y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
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2x\(\frac{dy}{dx}\) + y(\(\frac{dy}{dx}\))² – y
Explanation
y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
Which of the following is the general solution of \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + y = 0
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y = (Ax + B)e
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y = Ae + Be
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y = A cos x + B sin x
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None of the above
Explanation
y = (Ax + B)e
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