Question

(1 point) Mark all of the possibilities that can arise when solving a quadratic equation as in the method of solving order 2 Cauchy-Euler equations. е A. One repeated real root. B. Two distinct real roots. C. No roots D. One complex root. E. Two complex roots. F. One real root and one complex root. G. None of the above (1 point) To find , and u, we would need to integrate which of the following? Mark all that apply. yw A. A B. yf(x) w c. yW f(x) PD. () Y2 PE f(x) и f(x)W G. - Yvf(x) W H1f(x) w I. None of the above (1 point) Mark all of the following which are Cauchy-Euler equations. C CA. 7x²y" + 7xy' + 4y = ek B. 4x3 dr3 + 2x2y" – 3y = 0 C. xy(5) + 7x"y"+ 2y = 0 + 2ry" – 3y = 0 D. 483 dx3 DE. "x}3) + 7xe'y' + 8y = 0 OF. *?xy(3) + 7xy' + 8y = 0 OG. 7x+y" + 7xy' + 4y = 0) OH. x+y15) + 7x}," + 2y = 0 Ol. None of the above

Answer 1

(A) When selving of a quadratic equation as in the method Solving Order 2 Cauchy - Euler equations, we get auxiliary equation of the form . the ar²+bx+c=0 When b² - 4aco then One repeated real yout b²-4 acco then two complex roots. if is b²-4ac >o then Two distinct real rooks. Hence option A, B and E are correct. (B) if 4(x) = 419, +43 Yo be the salution of PCM) y" + 96x9 Y'+ 7648y = f(x) then. u, s yz . f(x) dx & Ug = s I. f(x) dx = w W Hence option B and I are correct. (C) The The general form of Cauchy - Euler equctions. appe? yn + an, xayot is n-1 + a Where ao y = f(x) ao, ai, az ani, an are constant +44 = ex 7x²4" + 7x 4 +44 asys +7x34" +2y= n7 x3y² + 7x4 + 8y = 72 7" + 724 +44 =O =0 all are Cauchy Eulex equatron. Hence A, e, f and G are correct.