Question

y'=\frac{x^2+3xy}{3x^2} (a) Prove the given first order ordinary differential (ODE) equation are, (i) Linear ODE equation (3 marks) (ii) Homogeneous ODE equations (3 marks) (b) Solve the given first order ordinary differential equation using, (i) Linear ODE equation (6 marks) (ii) Homogeneous ODE equations. (10 marks) (c) Calculate the particular solution, for the initial condition of y(1) =1. (3 marks) Q2 Second-order non-homogeneous ODE is given as: y''-y'-12y=5e^{4x} (a) By using undetermined coefficient method, (i) Find the complimentary function, $y_c$, for the corresponding homogeneous equation. (2 marks) (ii) Determine the particular integral, $y_p$. (7 marks) (iii) Write the general solution for the second order non-homogeneous ordinary differential equation with initial condition y(0) = y'(0) =1. (6 mark) (b) Calculate the general solution by using method of variation of parameter. (10 marks)

          y'=\frac{x^2+3xy}{3x^2}
(a) Prove the given first order ordinary differential (ODE) equation are,
(i) Linear ODE equation
(3 marks)
(ii) Homogeneous ODE equations
(3 marks)
(b) Solve the given first order ordinary differential equation using,
(i) Linear ODE equation
(6 marks)
(ii) Homogeneous ODE equations.
(10 marks)
(c) Calculate the particular solution, for the initial condition of y(1) =1.
(3 marks)
Q2 Second-order non-homogeneous ODE is given as:
y''-y'-12y=5e^{4x}
(a) By using undetermined coefficient method,
(i) Find the complimentary function, $y_c$, for the corresponding homogeneous
equation.
(2 marks)
(ii) Determine the particular integral, $y_p$.
(7 marks)
(iii) Write the general solution for the second order non-homogeneous ordinary
differential equation with initial condition y(0) = y'(0) =1.
(6 mark)
(b) Calculate the general solution by using method of variation of parameter.
(10 marks)

y'=(x^2+3xy)/(3x^2)
(a) Prove the given first order ordinary differential (ODE) equation are,
(i) Linear ODE equation
(3 marks)
(ii) Homogeneous ODE equations
(3 marks)
(b) Solve the given first order ordinary differential equation using,
(i) Linear ODE equation
(6 marks)
(ii) Homogeneous ODE equations.
(10 marks)
(c) Calculate the particular solution, for the initial condition of y(1) =1.
(3 marks)
Q2 Second-order non-homogeneous ODE is given as:
y”-y'-12y=5e^4x
(a) By using undetermined coefficient method,
(i) Find the complimentary function, yc, for the corresponding homogeneous
equation.
(2 marks)
(ii) Determine the particular integral, yp.
(7 marks)
(iii) Write the general solution for the second order non-homogeneous ordinary
differential equation with initial condition y(0) = y'(0) =1.
(6 mark)
(b) Calculate the general solution by using method of variation of parameter.
(10 marks)

Added by Jerry G.

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