4. Consider this second order linear differential equation 2d¢y _5r° dy +8y 0 dr dr2 =...
please help dy 1. Solve the initial value problem, dr2 8y-16% y(0) = 5, 7(0) = 0. de
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
Given a second order linear homogeneous differential equation a2(x)” + a (x2y + a)(x2y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, y. But there are times when only one function, call it yi, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the az(x) + 0 we rewrite...
Consider the differential equation: y' - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cı and ca to denote arbitrary constants. Enter ci as c1 and ca as c2. Yc = cle cle5x - + c2 b. Apply the method of undetermined coefficients to find a particular solution. yp er c. Solve the initial value problem corresponding to the initial conditions y(0) = 6 and y(0) = 7. Give...
C. This problem is about the inhomogeneous equation dy (1-)2 (1+ x) dy (1-3) (I) y=re +x dr dr2 and the corresponding homogeneous equation dy dy +x dr2 (1- r) (H) -y 0. dr (i) Show that y=r and y= e are solutions of (H). (ii) From (), the general solution of (H) must be y= Ar + Be for arbitrary constants A and B. Solve (I) by the variation of parameters method of Lesson 22, i.e., setting y ur...
Find the particular solution of the following first order linear differential equation dy dr - Y= CON 2 Fe2r,y(0) = -1
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
The answer above is NOT correct. (1 point) Find the general solution to y(4) – 8y"" + 15y" = 0. In your answer, use C1,C2,C3 and C4 to denote arbitrary constants and x the independent variable. Enter ci as c1, c2 as c2, etc. y=c1+xc1+c3e^(3x)+c4e^(5x) help (equations)
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...