Which of the following is the correct option for the equation \frac{{dy}}{{dt}} + \,( - 1)y = \,6file:///C:/Users/MUHAMM~1.SHA/AppData/Local/Temp/ksohtml5460/wps12.jpgusing phase diagram?

• A) The inter temporal equilibrium will be convergent
• B) It can be solved with the Bernoulli equation method
• C) The inter temporal equilibrium will be unaffected
• D) The inter temporal equilibrium will be divergent

Which of the following is the correct option for the dynamic stability of the time-path of i(t) = [i(0) - (\frac{{\alpha + \gamma }}{{\beta + \delta }})]{e^{\frac{{\beta + \delta }}{{\rho - \sigma }}t}}{\mkern 1mu} + \frac{{\alpha + \gamma }}{{\beta + \delta }}

• A) None of the given options
• B) The complimentary function will not converge to particular solution
• C) The particular function will converge to complementary solution
• D) The complementary function will converge to particular solution

Which of the following is the correct option for the marginal product of labor and capital, MPk= 5L and MPL= 1.2 LK ; assuming it is on an Iso-quant (dQ=0) ?

• A) It is the general solution of the second order homogeneous differential equation
• B) If it is exact differential equation, it will be solved in four steps
• C) It is the definite solution of the first order homogeneous differential equation
• D) If it is inexact differential equation, it will be solved in four steps

Which of the following is the incorrect option for the equation, \,\frac{{dy}}{{dt}} + \,\frac{\alpha }{\beta }Y = \,\frac{{{M_s}}}{\beta } ?

• A) It is first order second degree differential equation
• B) The equation cannot be resolved using differential equation method
• C) It is first order first degree differential equation
• D) It is a modified form of elasticity of money demand and money supply

Which of the following is the correct option for equation \frac{{dy}}{{dt}} + \,2ty = 4t ?

• A) It is the general solution of the first order non homogeneous differential equation
• B) It is the definite solution of the first order homogeneous differential equation
• C) It is the first order non homogeneous differential equation with variable coefficient term
• 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<1?

• A) All of the given options
• B) It is a non linear differential equation where Ym causes non linearity
• C) It is a linear differential equation of first order
• D) It is a non linear differential equation where Ry causes non linearity

Which of the following is the incorrect option for equation if value of file:///C:/Users/MUHAMM~1.SHA/AppData/Local/Temp/ksohtml1148/wps5.jpg is negative Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta + \tau \beta - \delta }})]{e^{\frac{{1 - \beta + \tau \beta - \delta }}{\gamma }t}}\, + \frac{\alpha }{{1 - \beta + \tau \beta - \delta }} ?

• A) All of the given options
• B) There will be convergence towards complementary solution
• C) There will be no convergence towards particular solution
• D) There will be divergence from the particular solution

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

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

Which of the following is the correct option for the capital function, K(t)= 100(2t+4)2 ?

• A) It represents the time path of the capital stock over time
• B) It is definite solution of linear first order differential equation
• C) It is definite solution of non linear differential equation
• D) It represents the time path of the GDP over time

Which of the following is the incorrect option for the money market equation, \(\alpha Y\, + \,\beta \frac{{dy}}{{dt}} = \,{M_s}\) ?

• A) All of the given options
• B) The value of income (Y) will be inversely related money supply (Ms)
• C) The value of money supply (Ms) will be constant
• D) The standard first order differential equation can be used

Which of the following is the correct option for the equation,V(t) = 1000e-0.04t +V(0) ?

• A) It is first order first degree differential equation with definite solution
• B) The equation represent a modified form of elasticity of oil extraction
• C) It is first order differential equation with general solution
• D) It is homogeneous first order differential equation

Which of the following is the correct option for the marginal product of labor and capital, MPk= 3LK and MPL= 5LK ; assuming it is on an Iso-quant (dQ=0) ?

• A) The values cannot be used to apply the exactness test
• B) There will be three steps involved if it is exact differential equation
• C) It is a non linear first order homogeneous differential equation
• D) It is first order non homogeneous differential equation

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

• A) Time path is not involved in the equation
• B) The value of \(\frac{\alpha }{{1 - \beta - \delta }}\) is the particular solution of the equation
• C) The value of \(\frac{\alpha }{{1 - \beta - \delta }}\) = 0 will ensure convergence towards equilibrium value
• D) The value of \(\frac{\alpha }{{1 - \beta - \delta }}\) >0 will ensure convergence towards equilibrium value

Given the equation for rate of consumption \(\frac{{dC}}{{dt}}\) = -4C+10 , Which of the following is the incorrect option?

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

Which of the following is the incorrect option for national income equation \frac{{dy}}{{dt}} + (\frac{{1 - \beta + \tau \beta - \delta }}{{ - \gamma }})Y = - \frac{\alpha }{\gamma } ?

• A) None of the given options
• B) It has only the particular solution
• C) It has both complementary and particular solutions
• D) It is first order differential non homogeneous equation

Which of the following is the correct option for the \({y^{ - m}}\frac{{dy}}{{dt}} + \,R{y^{1 - m}} = \,T\) assuming m>1?

• A) None of the given options
• B) It is first order homogeneous differential equation
• C) If it is inexact differential equation, it will be solved in four steps
• D) It is a non linear differential equation which have been converted from linear equation

Which of the following is the correct option for the equation \frac{{dy}}{{dt}} + \,(3)y = \,5 using phase diagram?

• A) The inter temporal equilibrium will be unaffected
• B) The inter temporal equilibrium will be convergent
• C) It can be solved with the Bernoulli equation method
• D) The inter temporal equilibrium will be divergent

Which of the following is the correct option for the dynamic stability of the time-path of rate of change of population; dN/dt = 0.01 N and N(t) 40000e0.017t ?

• A) The particular function will converge to complementary solution
• B) It is first order homogeneous differential equation
• C) The complementary function will converge to zero
• D) The complimentary function will converge to particular solution

Which of the following is the correct option for the dynamic stability of the time-path of i(t) = [i(0) - (\frac{{\alpha + \gamma }}{{\beta + \delta }})]{e^{\frac{{\beta + \delta }}{{\rho - \sigma }}t}}{\mkern 1mu} + \frac{{\alpha + \gamma }}{{\beta + \delta }} ?

• A) The time path should be equal to the particular solution
• B) The time path should diverge from the particular solution
• C) The time path should converge towards the complementary solution
• D) There is a particular solution to the equation

Which of the following is the correct option for the {y^{ - m}}\frac{{dy}}{{dt}} + \,R{y^{1 - m}} = \,T assuming m>1?

• A) It is first order homogeneous differential equation
• B) None of the given options
• C) If it is inexact differential equation, it will be solved in four steps
• D) It is a non linear differential equation which have been converted from linear equation