Question

Use the method of Laplace transforms to solve the initial value problem for it dr-*+y. x(0) = 0,0) = 1

Answer 1

n(^) =0, y6):d. : 21 on both si deo of the giren Taking dglace tranoform we have, equationo, a(a') = - d(a) + dl) d (y) = 2a(^). or, polte) - x(0) : -& (») + L(y). paly) - ylo) = 2 d (a) %3D %3D %3D 2a(x) - pa(y) = -1. or, 2(p+s)a(@) - 2 ly)=0, 2(p1)d(4) - p(prs)X » (p*a p-2)<(y): p+1 pap-2

y@)= . n(0):0, (say) p+2 (A+6)p +(26-A) p**p-2 P-L (p+2)(p-1) m) p?xp-2 mporing the Coeffiient of P, and the Conotant term from th numerators of both sides, we have, A+B÷1, 2B-A =d -> A=3,B=. p+1 L4)= pz+p-2 Now %3D -2t of