Question

form the differential equation from primitive y=a sinx +b cosx+x sinx, where constants are arbitrary?

Answer 1

 any point = | y dy/dx|

So differentiating with respect to x we get,

y dy/dx = ±8 ⇒ y dy = ±8 dx ⇒ y 2/2 =   ±8x + c

y2 = 16 x+2c1, if c1= -8    or 

y2 = -16x +2c2, and c2= 24

Hence  (A), (B) are  correct answers.

2. Equation of a curve that would cut x2 + y2 - 2x - 4y - 15 = 0 orthogonally can be;

(A) (y-2) = l(x-1)                                                 (B) (y-1) = l(x-2)   

(C) (y+2) = l(x+1)                                                   (D) (y+1) = l(x+2)   where l ∈R.

Solution: Any line passing through the center of the given circle would meet the circle orthogonally.

Hence (A) is the correct answer.

3. Let m and n be the order and the degree of the differential equation whose solution is y = cx +c2- 3c3/2 +2, where c is a parameter. Then,