Solve the following initial value problem for r as a function of t. Differential equation: at2 =e'i-2elj+27e3k Initial conditions: r(0) =3i + 2j + 7k dr dt t= 0 = -i+ 5j . . . Tillu ule yetI al di luuelIvauve. CA. r(t ) = (e + Cx1+ + (x2) i+ ( - ze"* + cyst+ cy2)i+ (3e31 + cz1t+ O B. r(t) = (e' + (x1t + (x2) it ( - ze"t - cyst+ Cy2)i+ (3e31 + cz1t+0 O C. r(t) = eli+ 2e- j+ 9ek + C O D. r(t) = eli-2e- j+ ge3*k + C Solve the initial value problem for r as a vector function of t. r (t ) = e - 2t+ 2 Ji+ (-2e +t+7|j+ 3es- 9t + 3|k