need code in c

with explanation please

Objective: Create a C script that will find the Zero-Input Response of a Second order Linear Time Invariant System Dy a,Dy+a, -0 based on coefficients (a, and a,) and initial conditions (y(0) and y(0)). (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 arder nontrivial solution Create a header file for this step. 3) Based on the rootsA, and A of the second order system, your script should decide air roots(Ks) are nonrepeating real , the response ylt) is vtt)- C,el Ce for to. Find C's and display your yit) on screen b) If roots [A's) are repeating real (A-A,), the response y(t) is it)-(, tater, for t:0 Find C's and display your yit) on screen c) if roots [A's) are complex conjugate('s- and a jB), the response yt) is vit-C"cospt +9), for t20. 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 e