If f''(0) = k, k ≠ 0, then the value of limx→0 2f(x) - 3f(2x) + f(4x)x2 is
k
2k
3k
4k
If y = emsin- 1x then 1 - x2d2ydx2 - xdydx - ky = 0, where k is equal to
m2
2
- 1
- m2
Solution of x + y2dydx = a2 ( 'a' being a constant) is
x + ya = tany + Ca, C is an arbitrary
xy = atanCx, C is an arbitrary
xa = tanyC, C is an arbitrary
xy = tan(x + C), C is an arbitrary
The integrating factor of the first order differential equation
x2x2 - 1dydx + xx2 + 1y = x2 - 1 is
ex
x - 1x
x + 1x
1x2
Let a and B be the roots of x2 + x + 1 = 0. If n be a positive integer, then αn + βn is
2cos2nπ3
2sin2nπ3
2cosnπ3
2sinnπ3
For real x, the greatest value of x2 + 2x + 42x2 + 4x + 9 is
1
12
14
If the solution of the differential equation xdydx + y = xex be xy = exϕ(x) + C, then ϕx is equal to
x + 1
x - 1
1 - x
x
The order of the differential equation of all parabolas whose axis of symmetry along X-axis is
3
None of these
General solution of ydydx + by2 = acosx, 0 < x < 1 is
y2 = 2a2bsinx + cosx + ce- 2bx
4b2 + 1y2 = 2asinx + 2bcosx + ce- 2bx
4b2 + 1y2 = 2asinx + 2bcosx + ce2bx
The integrating factor of the differential equation
1 + x2dydx + y = etan-1x is
tan-1x
1 + x2
etan-1x
loge1 + x2