requirements a) Perform the quantitative analysis (finding solutions analytically) of Eq. (3). For q=1.901 and q=1.301 with a = 12, β=0.52,8=4.3396,1=0.34 and U =4.9. b) Perform the quantitative analysis (finding solutions analytically) of Eq. (3). For q=1.101 and q=1.201 with a 3.35, B=0.381,8=1.34,1=0.2 and U = 2.4 c) Reduce this second order differential Eqs. into system of differential equations, d) Perform the qualitative analysis (finding equilibrium points, eigenvalues and drawing phase portraits) of Eq. (3) keeping the parameter values same as in part (a) and (b). e) Plot the solutions obtained analytically

a) To perform the quantitative analysis of Eq. (3), we will substitute the given values into the equation. For q=1.901 and q=1.301, with a=12, β=0.52, γ=4.3396, λ=0.34, and U=4.9.

b) Similarly, for q=1.101 and q=1.201, with a=3.35, β=0.381, γ=1.34, λ=0.2, and U=2.4.

c) To reduce the second-order differential equation into a system of differential equations, we will use appropriate substitutions and transformations.

d) For the qualitative analysis, we will find the equilibrium points, eigenvalues, and draw phase portraits of Eq. (3) using the parameter values from parts (a) and (b).

e) Finally, we will plot the solutions obtained analytically for the given equations.