DIFFERENTIAL EQUATION-CW1
1 INFOMATHS/MCA/MATHS/
BHU-2015
1.The order of a differential equation is defined as :
(a) the power of highest derivative in the equation
(b) the power of lowest derivative in the equation
(c) the order of lowest derivative occurring in the equation
(d) the order of highest derivative occurring in the equation
2.The degree of the differential equation:
(a) 6(b) 5(c) 4(d) 3
3.The solution of is given by :
(a) cy = xey-x(b) cx = yey-x
(c) cy = xex-y(d) cx = yex-y
4.Which one of the following differential equations is linear :
(a)
(b)
(c)
(d)
5.Which one of the following provides a general solution of the differential equation sec2x tan y dx + sec2 y tan x dy = 0?
(a) tan x tan y = c (b) tan x + tan y = c
(c) sec x sec y = c (d) sec x + sec y = c
PUNE-2015
6.Consider the differential equation
(a) Every solution of equation is identically zero
(b) All solutions of equation are unbounded
(c) All solutions of equation approaches to zero when x
(d) No solution of equation approaches to zero when x
7.For what value of k the line y = 9x be the tangent to the curve at some point on the xy-plane with constraint that x > - 1
(a) k < 0 (b) k > 0 and k < 1
(c) k > 1 and k < 3 (d) k > 3
8.Find the differential equation of the curve after eliminating arbitrary constants.
(a) (b)
(c) (d)
HCU-2015
9.Which is the solution of the differential (x4ex – 2xy2) dx + 2x2ydy =
(a) (b)
(c) (d)
10.A curve y(x) is passing through the point (1, /4) and its slope at any point (x, y) is , then the equation of the curve is
(a) y(x) = x tan-1 (log(e/x))
(b) y(x) = tan-1 (log(e/x))
(c) y(x) = x tan-1 (log(x/e))
(d) N.O.T
MP-2015
11.The solution of is given by
(a) y = e4x + x2 + C (b)
(c) y = e3x + C (d) y = e-3x + 6x + C
12.The solution of is
(a)
(b)
(c) y = sin (x + y) + C
(d) tan (y + x) = x + sec x + C
13.The differential equation of all non-vertical lines in a plane (ax + by = 1, b 0) is
(a) (b)
(c) (d)
14.The solution of (x + y)dx + xdy = 0 is given by
(a) x2 + y2 = C (b) 2x2 – y2 = C
(c) x2 + 2xy = C (d) y2 + 2xy = C
15.The solution of differential equation satisfying y(1) = 1 is
(a) y2 = x2 – 2x + 2 (b) y2 = 2x2 – x – 1
(c) y = x2 – 2x + 2 (d) y2 = x + 2
16.The integrating factor of the differential equation
is given by
(a) 2logx (b) x2
(c) x2/3(d) x-2/3
17.The solution of the differential equation
is given by
(a) ey = ex + C (b) (x + y)ey = ex + C
(c) ey = (x + 1)ex + C (d) y = (x + 1)log x + C
18.The solution of differential equation
is given by
(a)
(b)
(c)
(d)
19.The solution of differential equation
is given by
(a) (b) y = x2ey + C
(c) (d)
20.The solution of differential equation
is given by
(a)
(b)
(c)
(d)
PUNE-2014
21.The differential equation xdy – ydx = 0 represents
(a) parabola (b) straight line
(c) circle (d) hyperbola
DU-2013
22. Which of the following statement is TRUE?
(A) y' = x/y is a first order linear differential equation
(B) y” + (y')3 + y = 0 is a nonlinear differential equation of order 3
(C) y" + y' +y = x is a homogenous second order differential equation
(D) (sin x) y" + (1 – x2)y' + (cos x) y = 0 is a second order linear differential equation
Answers
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10D / A / Bc / D / A / C / A / B / A
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
C / B / D / C / A / D / B / C / A / B
21 / 22
- / -
Solutions
BHU-2015
1.Ans. (d) The order of differential equation is defined as the order of highest derivative occurring in equation.
2.Ans. (a) We have,
Hence, degree of the given differential equation is 6.
3.Ans. (b, c) We have,
y + log y = x + log x + c
log y – log x = x – y + c
y = cxex-y
cy = xex-y or cx = yey-x
4.Ans. (d)
is a linear differential equation.
5.Ans. (a) We have,
secxtan y dx + sec2y tan y dy = 0
tan x. tan y = c
PUNE-2015
6.Ans. (c) We have,
log y = - 2x + c
y = Ae-2x
Hence, all solution of equation approaches to zero when x
7.We have,
8.Ans. (a) We have, y = aebx
HCU-2015
9.Ans. (b) (x4.ex – 2xy2)dx + 2x2y dy = 0
Multiplying both sides by 2y.
Take y2 = z
Comparing with
Here, , Q = - x2.ex
Factor
Solution is given as
Z. If
10.Ans. (a)
Let
tanV = - log |x| + c
y = x tan-1 (log (e/x))
MP-2015
11.Ans. (c) Given,
y = e3x + C
12.Ans. (b) Given,
On putting x + y = z
Now,
13.Ans. (d) Given equation of line is ax + by = 1.
On differentiating w.r.t. x, we get
Again, on differentiating,
14.Ans. (c) Given differential equation is
(x + y) dx + xdy = 0
IF
Then, the solution is
x2 + 2xy = C
15.Ans. (a) Given differential equation is
y dy = (x – 1) dx
When x = 1, y = 1
1 = C
Therefore, the solution is
y2 = x2 – 2x + 2
16.Ans. (d)
y-1/3 = z
IF
17.Ans. (b) Given differential equation is
(x + y) dy + dy = (ex – y) dx
ey [(x + y)] dy + eydy = exdx
(x + y)ey = ex + C
18.Ans. (c)
19.Ans. (a)
20.Ans. (b)
PUNE-2014
21.
DU-2013
22.
1 INFOMATHS/MCA/MATHS/