Problem 1a. Verify that the given functions form a fundamental set of solutions of the differential equation.
4y'' + 36y = 0; y1 = cos(3x); y2 = sin(3x)
Problem 1a. Verify that the given functions form a fundamental set of solutions of the differential...
Verify that the given function form a fundamental set of solutions on the interval (0, 0), compute the Wronskian, and form the general solution. xy'' – 6xy' +12y = 0 x?; x+ I verified the solution. ONo Yes Find the Wronskian and verify that the functions are linearly independent on the interval (0, 0). W(x", x4) = 0 Preview I found the general solution. OYes ONO
Differential equations / which pair of functions below cannot be a fundrmental set of solutions? 6. Which pair of functions below cannot be a fundamental set of solutions? (8 Points) 1, x3, xinx 3 cost + 6 sint, 5 cost + 10 sint €2x cos 3x + sin 3x, 1 e-31 3 te-31 5et + 5, 2e + 1
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, 0). Find the general solution of the given nonhomogeneous equation. *?y" + xy' + (x2 - 1)y = x3/2; Y1 = x-1/2 cos(x), Y2 = x-1/2 sin(x) y(x) =
Two linearly independent solutions of the differential equation y" + 4y' + 5y = 0 are Select the correct answer. a. Y1 = e-cos(2x), y2 = eʼsin (2x) b. Y1 = e-*, y2 = e-S* c. Yi= e-*cos(2x), y1=e-* sin(2x) d. Y1 = e-2xcosx, x, y2 = e–2*sinx e. Y1 = e', y2 = 5x
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E. a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are Select the correct answer. 7 Oa yı = e-*cos(2x), Y1 = e-*sin(2x) Ob. Y1 = et, y2 = ex Oc. yı = e cos(2x), y2 = e* sin(2x) Od. yı=e2*cosx, y2 = e2*sinx Oe. y = e-*, y2 = e-S*
Differential equations for engineering I need the final answer please Verify by substitution that the given functions form a basis. Solve the given initial value problem y" + 18y' +90y = 0, -** cos (3x), e-% sin (3x), y(0) = 1, y (0) = -9 Enclose arguments of functions in parentheses. For example, sin (29x). Use an asterisk. * to indicate multiplication. For example, 2* f (x).a*** (x+b) * (c**+ d), b * tan(a *) or e(*) * b. Q
6. Which pair of functions below cannot be a fundamental set of solutions? * (8 Puan) O 1, x, x? Inx O 5e + 5, 2eX + 1 0 2x, cos 3x + sin 3x, 1 3 cost + 6 sint , 5 cost + 10 sint O e-31, te-31
1. (20 pts.) In the following Problems: (a) Seek power series solutions of the given differential equation about the given point xo ; find the recurrence relation. (b) Find the first four terms in each of two solutions yi and y2 (unless the series terminates sooner). (c) By evaluating the Wronskian W(y1, y2)(xo), show that yı and y2 form a fundamental set of solutions. (d) If possible, find the general term in each solution. i) y" +k+x+y = 0, 40...
Verify that the given functions Y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. x2y" – 3xy' + 4y = 7x? In x, x>0; 71(x) = x2, yz(x) = x2 In x Y(x) =