Study Set Content:
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
What is the differential equation of all straight lines.
A. y' =0
C. y" =0
B. y' 1
D. y'infinity
C. y" =0
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
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
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
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
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
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
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
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
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
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 )
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
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
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
