Which of the following is the incorrect option the equation $y(t) = \,A{e^{\int {u(t)\,dt} }}$ ?

• A) All of the given options
• B) It is the general solution of the second order homogeneous differential equation
• C) It is the definite solution of the first order homogeneous differential equation
• D) It is the definite solution of the first order non homogeneous differential equation

Which of the following is the correct option for second order differential equation with constant coefficient and variable terms i.e L.H.S is the f(t)?

• A) It will change both complementary and particular solution
• B) The value of particular solution cannot be calculated
• C) It will change the complementary solution
• D) It will change the particular solution

Which of the following is the correct option for $\frac{{dP}}{{dt}}\, \propto$ (Qd - Qs)?

• A) Price adjustments are directly proportional to excess/shortage of demand
• B) Price adjustments are inversely proportional to excess demand
• C) Price adjustments are inversely proportional to excess supply
• D) Price adjustments are directly proportional to equilibrium quantity

Which of the following is the correct option for the dynamic time path of the market price, P(t) = [P(0)-P*]e-kt + P* ?

• A) P(t) will converge towards P* regardless of value of P(0)
• B) There is a particular solution to the equation
• C) There is a complementary solution to the equation
• D) All of the given options

Which of the following is the correct option for the dynamic stability of price equation; When n>0 ?$P'' + \frac{m}{n}p' + [ - \frac{{\beta + \delta }}{n}]P = - \frac{{\alpha + \gamma }}{n}$

• A) The system will be dynamically undefined
• B) The system will dynamically unstable with A1 = 0 and A2 >0
• C) The system will dynamically stable with A1 = 0
• D) The system will dynamically stable with A1 >0 and A2 = 0

The time path should converge towards the complementary solution for dynamic stability in the pollution function given by P(t) = 30e-0.2t ?

• A) True
• B) False
• C)
• D)

Which of the following is the incorrect option for the deposit function, D(t) = 4000e-0.05t +20 ?

• A) It is first order differential non homogeneous equation
• B) It has both complementary and particular solutions
• C) It will converge towards to the particular solution
• D) It will diverge from the equilibrium value

Which of the following is the correct option for y’’(t) + 3y = 0 ?

• A) The particular solution will be equal to three
• B) It is a non homogeneous second order differential equation
• C) The particular solution will be equal zero
• D) It is a homogeneous first order differential equation

Which of the following is the correct option for Fuel usage equation, F(t) = 12000e-0.001t - 6000 at time t=0?

• A) Fuel usage F(t) will be 12000 litre
• B) Fuel usage F(t) will be 18000 litre
• C) Fuel usage F(t) will be 6000 litre
• D) Fuel usage F(t) will be 4000 litre

Which of the following is the incorrect option for the equation, $\frac{{dy}}{{dt}} + \,u(t).y = 0$ ?

• A) All of the given options
• B) The equation will have no definite solution
• C) It is first order differential equation with general solution
• D) It is first order first degree non homogeneous differential equation

Which of the following is the correct option in the utility equation, 3xy.dx+x.dy=0 ?

• A) It is the definite solution of the first order non homogeneous differential equation
• B) It is first order non homogeneous differential equation
• C) None of the given options
• D) The equation cannot be used for the exactness test

Which of the following is the incorrect option for the possible cases of Phillips equation dπ/dt = j (p - π) ?

• A) j > 1
• B) j ><0
• C) j = 0
• D) j > 0

Which of the following is the incorrect option for second order differential equations with α12 - 4α2 <0 ?

• A) It will have distinct real roots
• B) It will have both repeated and real roots
• C) It will have repeated real roots
• D) All of the options

Which of the following is the incorrect option for the dynamic time path of the money market , P(t) = [ P(0) - Ms/αY] e-(αjY)t + Ms/αY ?

• A) The deviation will converge towards particular solution if αj>0
• B) The particular solution is equal to P(0)
• C) There is a particular solution to the equation
• D) There is a complementary solution to the equation

Which of the following is the incorrect option for $\frac{{dP}}{{dt}}$= j(Qd - Qs) ?

• A) The value of j will be negative
• B) All of the given options
• C) The value of j will be zero at equilibrium point
• D) The value of j is known as adjustment coefficient

Which of the following is the correct option in the equation, y''(t)+a1y' +a2y = b if b<0 ?

• A) None of the given options
• B) It is first order homogeneous differential equation
• C) It is a non linear differential equation
• D) It is second order second degree differential equation

Which of the following is the correct option for equation if value of γ is negative $Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta - \delta }})]{e^{\frac{{1 - \beta - \delta }}{\gamma }t}}{\mkern 1mu} + \frac{\alpha }{{1 - \beta - \delta }}$ ?

• A) There will be convergence towards complementary solution
• B) There will be no convergence towards particular solution
• C) There will be no impact of the convergence mechanism
• D) None of the given options

Given the equation for rate of investment I’(t) = 0.05I+90, Which of the following is the incorrect option?

• A) It is a case of non homogeneous first order differential equation
• B) There is a particular solution to the equation
• C) It is a case of non homogeneous second order differential equation
• D) All of the given options

Which of the following is the correct option for the $\frac{{dy}}{{dt}} + \,Ry = \,T{y^m}$ assuming m=0?

• A) The value of the equation will not depend on time
• B) It will be a first order linear differential equation
• C) There will be not general solution for the equation
• D) It is a non linear first order homogeneous differential equation

Which of the following is the incorrect option for the equation,$\frac{{dY}}{{dt}} + \frac{{1 - \beta + \tau \beta - \delta }}{\gamma }Y = \frac{\alpha }{\gamma }$?

• A) It is first order third degree differential equation
• B) It is first order second degree differential equation
• C) All of the given options
• D) The equation represent a modified form of elasticity of investment