Question

All I need answered is C

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. 270 if Osts 7n/6 y'' + 6y' +45y = g(t); y(0) = 0, y' (O) = 0, where g(t) = 0 if t>7n/6 Complete parts (a) through (c) below. The solution for Osts 7t/6 is y(t) = e -3t( - 6 cos 6t - 3 sin 6t) +6. (Type an equation.) (b) Find a general solution for t> 71/6. The general solution for t>71/6 is y(t) = e -36 (C4 cos 6t+c, sin 6t) (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= 71/6. This gives a piecewise continuously differentiable function that satisfies the differential equation except at t = 7n/6. if Ost<7n/6 The solution to the differential equation is y(t) = if t>70/6

Answer 1

Giveni y"+byl + usy = g ty i g (0)=0; y'(o)=0 g(+) if os tLaTVG in if it 77% ylt) as -34 - 6 cos 6t in 3 sin6t) + 6 b) 8 (+) = -3t ville (c, cofft + C₂ sinot) y(0)20 디 g'le) = sebe *[-6cı sin64 +662696eft. crosott Casinst) ylco) 6C2-34, > [c2=0 -36-37 €3* CC → os y CF ) = e 37 (-6c0f6t-3 sinbt) + 6 olt!? lif t> 7% * If I am able to convince you then one Like takes one second only, Thanks :- a lot.