MATH 2214 Midterm: MATH 2214 Virginia Tech 3.5 Exam
Document Summary
Y( /2) = c1 + c2 = 4, y ( /2) = c1 + c2 = 0. Solutions 3. 5: a) 2(cos( /3) + i sin( /3)) = 1 + i 3, 2 2(cos( /4) i sin( /4)) = 2 + 2i, (2 i)( i) = 1 2i, 1/(2 2)( . 3/2 i/2) = : 4 exp(2 i/3) = 4( 1/2 + i 3/2) = 2 + 2i 3, a) 9 2 + 1 = 0, i. e. = i/3, y = c1 cos(t/3) + c2 sin(t/3). c) This leads to c2 = e /2, c1 = 3e /2: a) 9 2 + 2 = 0, i. e. = i /3, y = c1 cos( t/3) + c2 sin( t/3). c) y(3) = c1 = 2, 3 c2 = . y (3) = . This leads to c1 = 2, c2 = 3: we have.
