On putting y = vx; homogeneous differential equation x²dy + y(x + y)dx = 0 becomes ______

(a)

x dv + (2v+v²)dx = 0

(b)

v dx + (2x+x²)dv = 0

(c)

v² dx-(x+x²)dv = 0

(d)

v dv + (2x+x²)dx = 0

The I.F. of \(\frac { dy }{ dx } \)- y tan x = cos x is _____

(a)

sec x

(b)

cos x

(c)

e^tanx

(d)

cot x

The P.I. of (3D²+D-14)y = 13 e^2x is ______

(a)

26x e^2x

(b)

13x e^2x

(c)

xe^2x

(d)

\(\frac { { x }^{ 2 } }{ 2 } \)e^2x

The P.I. of the differential equation f(D)y = e^ax where f(D) = (D-a) g(D), g(a) ≠0 is _____

(a)

me^ax

(b)

\(\frac { { e }^{ ax } }{ g(a) } \)

(c)

g(a)e^ax

(d)

\(\frac { xe^{ ax } }{ g(a) } \)

The equation of ydx + xdy = e^-xy dx if it cuts the Y-axis is ______

(a)

e^xy

(b)

e^xy = c

(c)

e^xy = x + 1

(d)

e^xy = y + 1