Using C++,

Objective: Create a C script that will find the Zero-Input Response of a Second order Linear Time Invariant System D'y+a,Dy+a2- 0 based on coefficients (a; and az ) and initial conditions (v(O) and y(O). (D-d/dt) Requirements: 1) The user should be prompted to type in coefficients of the Linear Systems and Two Initial Conditions. 2) Find the roots of the second order nontrivial solution. Create a header file for this step. 3) Based on the roots A, and A2 of the second order system, your script should decide a) If roots (K's) are nonrepeating real, the response yit) is Cet, for t:0. y(t) -Ce Find C's and display your y(t) on screen. b) If roots (V's) are repeating real (A, A), the response ylt) is y(t) (C,+Cate), for t20 Find C's and display your y(t) on screen. c) If roots (Xs) are complex conjugate (Ks y(t)-Ctcos(Bt+0), for t20. r+) and . ), the response y(t) is Find C and and display your y(t) on screen. For step 3, use conditionals.Also use user defined functions to compute C's and 9 Objective: Create a C script that will find the Zero-Input Response of a Second order Linear Time Invariant System D'y+a,Dy+a2- 0 based on coefficients (a; and az ) and initial conditions (v(O) and y(O). (D-d/dt) Requirements: 1) The user should be prompted to type in coefficients of the Linear Systems and Two Initial Conditions. 2) Find the roots of the second order nontrivial solution. Create a header file for this step. 3) Based on the roots A, and A2 of the second order system, your script should decide a) If roots (K's) are nonrepeating real, the response yit) is Cet, for t:0. y(t) -Ce Find C's and display your y(t) on screen. b) If roots (V's) are repeating real (A, A), the response ylt) is y(t) (C,+Cate), for t20 Find C's and display your y(t) on screen. c) If roots (Xs) are complex conjugate (Ks y(t)-Ctcos(Bt+0), for t20. r+) and . ), the response y(t) is Find C and and display your y(t) on screen. For step 3, use conditionals.Also use user defined functions to compute C's and 9