In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" +by' + cy=g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 100 if 0sts 5x/4 if t> 5π/4 y' +6y' +25y = g(t); y(0) = 0, y'(0) = 0, where g(t) = 0 Complete parts (a) through (c) below. (a) Find a solution to the initial value problem for Osts 5/4. The solution for Osts 5/4 is y(t)=-e-3t(4 cos (4t) + 3 sin (4t))+4. (Type an equation.) (b) Find a general solution for t> 5m/4. The general solution for t> 5x/4 is y(t) = 3 (C₁ cos (4t) + ₂ sin (4t)). (Type an equation. Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.) ... (c) Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first derivatives, at t=5/4. This gives a piecewise continuously differentiable function that satisfies the differential equation except at t= 5x/4. The solution to the differential equation is y(t) = -e-3t (4 cos (4t)+3 sin (4t))+4 if 0st<5/4 if t> 5x/4