1. Which of the following is the differential equation in the first order and first degree?

A. (y)+2y=-3

B.2Q 2Q дх ду 0

C.dy 9-x dx dy X

D.dx=-y+x

C.dy 9-x dx X y³

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What is the differential equation of all straight lines.

A. y' =0

C. y" =0

B. y' 1

D. y'infinity

C. y" =0

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The differential equation of all straight lines whose slope is m and whose y-intercept is b

A. y"-y=0

B. y' = 0

C. y"+y=0

D. y"=0

D. y"=0

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Write the differential equation of straight lines with slope an y-intercept equal?

A. ydx + (x-1) dy = 0

B ydx-(x+1)dy=0

C. xdy-(y+1) dx=0

D. ydy +(x+1) dx = 0

B. ydx-(x+1)dy=0

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What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis.

A. 2xdx + ydy = 0

B. 2xdy - ydx = 0

C. 4xdy + xdx = 0

D. 3xdy+2ydx = 0

B. 2xdy - ydx = 0

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What is the differential equation of circle whose center is at the origin?

A.xdy - ydx = 0

B. xdx + ydy = 0

C. x²dx + y²dy=0

D. y²dx + x²dy = 0

B. xdx + ydy = 0

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Find the orthogonal trajectory of family of curves xy = C.

A. x²-y²=C

B. e^(xy) = C

C. y = Cx²

D. x² + y² = C

A. x²-y²=C

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Solve the constant of integration of the given differential equation xdx + 6y5 dy = 0 considering x = 0 and y = 2:*L

C. 54

A. 46

B. 64

D. 120

B. 64

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Find the differential equation whose

general solution is y = C₁x + C₂e*.

A. y'' (x-1) - xy' + y =0

B. y' (x+1) + xy' + x = 0

C. y'' (x-1) + xy'+ y = 0

D. y' (x+1)+xy +x=0

A. y'' (x-1) -xy' + y =0

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Determine the solution of the following differential equation: y'+5y=0

A. y=5x+C

C. y = Ce^5x

B. y = Ce^ -5x

D. (A) or (B)

B. y = Ce^ -5x

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What is the solution of the equation dy/dx - 3y = 6?

A. y= Ce^(3x) - 2

B. y = Ce^(3x) + 2

C. y = Ce^(3x) - 4

D. y = Ce^(2x) - ½

A. y= Ce^(3x) - 2

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Find the general solution of y' = ysec x.

A. y = C (sec x - tan x)

B. y=C (sec x + tan x )

C. y=C (sec² x + tan x )

D. y = C(tan x - secx)

B. y=C (sec x + tan x )

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Find the general solution of sin x sin y dx + cos x cos y dy = 0

A. sin y = C cos x

B. sin x = C sin y

C. cos x = C x sin y

D. sin x = C x² cos y

A. sin y = C cos x

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Find the general solution of the given differential equation (2x-y) dx-(x+4y) dy = 0

A x² - 2y - xy = C

B. x2 + 2y + xy = C

C. x² - 2y² - xy = C

D. 2x²+ 2y + xy = C

C. x² - 2y² - xy = C

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Find the general solution of the given differential

equation (2x + 3y ) dx + (3x-y+5) dy = 0

A. 2x²+3xy + y²+15y = C

B. x²+6xy - y² + 12y = C

C. x² + 6xy + y² + 10y = C

D. 2x² + 6xy - y²+ 10y =C

D. 2x² + 6xy - y²+ 10y =C

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