In the formation of differential equation by elimination of arbitrary constants, after differentiating the equation with respect to independent variable, the arbitrary constant gets eliminated.

In the formation of differential equation by elimination of arbitrary constants, the first step is to differentiate the equation with respect to the dependent variable. Yes, the arbitrary constant gets eliminated after differentiation.

Which of the following is true with respect to formation of differential equation by elimination of arbitrary constants?

The given equation should be differentiated with respect to independent variable

Elimination of the arbitrary constant by replacing it using derivative

If ‘n’ arbitrary constant is present, the given equation should be differentiated ‘n’ number of times

To eliminate the arbitrary constants, the given equation must be integrated with respect to the dependent variable

A differential equation is given as
$${{\text{x}}^2}\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} - 2{\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{y}} = 4$$
The solution of differential equation in terms of arbitrary constant C₁ and C₂ is

$${\text{y}} = \frac{{{{\text{C}}_1}}}{{{{\text{x}}^2}}} + {{\text{C}}_2}{\text{x}} + 2$$

$${\text{y}} = {{\text{C}}_1}{{\text{x}}^2} + {{\text{C}}_2}{\text{x}} + 4$$

$${\text{y}} = {{\text{C}}_1}{{\text{x}}^2} + {{\text{C}}_2}{\text{x}} + 2$$

$${\text{y}} = \frac{{{{\text{C}}_1}}}{{{{\text{x}}^2}}} + {{\text{C}}_2}{\text{x}} + 2$$

The Head of a newly formed government desires to appoint five of the six elected members A,B,C,D,E and F to portfolios of Home,Power,Defence ,Telecom and Finance.F dose not want any portfolio if D gets one the five.C wants either Home or Finance or on portfolio.B says that if D gets either Power or Telecom then she must get the other one.E insists on a portfolio if A gets one. If a gets Home and C gets Finance,then which is NOT a valid assignment for Defence and Telecom?

B-Defence,D-Telecom

B-Defence,E-Telecom

F-Defence,B-Telecom

D-Defence,B-Telecom

A sum of Rs. 53 is divided among A, B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their share is gets. The ratio of their share is = ?

16 : 9 : 18

25 : 18 : 10

18 : 25 : 10

15 : 8 : 30

A sum of Rs. 76 is divided among A, B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 6 more than what C gets. The ratio of their share is gets. The ratio of their share is = ?

19 : 24 : 33

32 : 25 : 19

32 : 24 : 20

19 : 25 : 33

The figure shows the plot of y as a function of x

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

$$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} = 1$$

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = {\text{x}}$$

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - {\text{x}}$$

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \left| {\text{x}} \right|$$

How many arbitrary constants will be there in the general solution of a second order differential equation?

The number of arbitrary constants in a particular solution of a fourth order differential equation is __________________

If, A and B are arbitrary constants then what will be the differential equation of y = Ax + B/x?

x2 d2 y/dx2 – xdy/dx + y = 0

x2 d2 y/dx2 + xdy/dx + y = 0

x2 d2 y/dx2 + xdy/dx – y = 0

x2 d2 y/dx2 – xdy/dx – y = 0

The general solution of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 2\frac{{{\text{dy}}}}{{{\text{dx}}}} - 5{\text{y}} = 0$$ in terms of arbitrary constants K₁ and K₂ is

K1e(-1 + √6)x + K2e(-1 - √6)x

K1e(-1 + √8)x + K2e(-1 - √8)x

K1e(-2 + √6)x + K2e(-2 - √6)x

K1e(-2 + √8)x + K2e(-2 - √8)x