ULI ... W O SM L I VHU Application NST Summer Unde DS-11 Application. Dashbo In this problem you will use undetermined coefficients to solve the nonhomogeneous equation 7" + 6y' +9y = -(6te 3 +6e-9 + 18€ + 30) with initial values y(0) = -1 and 7(0) = -2. A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) 2+6r+90 B. Write the fundamental solutions for the associated homogeneous equation y = c (-31) = c21e-31) C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. Y A Y' – +B+C"20"(-3t)DI 30-31) B+0-313-32C-D)+2C1-3D(31) - 30032-18090)+1-12C+60)+2C) D. Write the general solution (Use of and c2 forcy and y o te (-31)+210-31)-6/3-21-312 -31) "30"-30) E. Plug in the initial values and solve for and oy to find the solution to the initial vale problem y-