Important Questions of Differential Equations Mathematics | Zigya

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41.

The differential equation which represents the family of curves given by tany = c(1 ex) is

  • extanydx + 1 - exdy = 0

  • extanydx + 1 - exsec2xdy = 0

  • ex1 - exdx + tanydy = 0

  • extanydy + 1 - exdx = 0


42.

Which one of the following is the differential equation that represents the family of curves y = 12x2 - c

where c is an arbitrary constant ?

  • dydx = 4xy2

  • dydx = 1y

  • dydx = x2y

  • dydx = - 4xy2


43.

Which one of the following is the second degree polynomial function f(x) where f(0) = 5, f( 1) = 10 and f(1) = 6 ?

  • 5x2 – 2x + 5

  • 3x2 – 2x – 5

  • 3x2 – 2x + 5

  • 3x2 – 10x + 5


44.

What is the degree of the differential equation

d3ydx3 + dydx2 - x2d4ydy4 = 0

  • 1

  • 2

  • 3

  • 4


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45.

Consider the following statements :

1) The function f(x) = ln(x) increases in the interval (0, ∞).

2) The function f(x) = tan(x) increases in the interval  - π2, π2

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


46.

The function u(x, y) = c which satisfies the differential equation x(dx – dy) + y(dy – dx) = 0, is

  • x2 + y2 = xy + c

  • x2 + y2 = 2xy + c

  • x2 - y2 = xy + c

  • x2 - y2 = 2xy + c


47.

If xmyn = am+n, then what is dydx equal to ?

  • mynx

  • - mynx

  • mxny

  • - nymx


48.

The solution of the differential equation dy = 1 + y2dx is

  • y = tan(x) + c

  • y = tan(x + c)

  • tan-1(y + c) = x

  • tan-1(y + x) = 2x


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49.

The order and degree of the differential equationkdydx = 1 + dydx223

  • 1 and 1

  • 2 and 3

  • 2 and 4

  • 1 and 4


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