(A) First find the fundamental system of solutions of the homogeneous equation
(b) Then Find the general solution of the equation
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(A) First find the fundamental system of solutions of the homogeneous equation (b) Then Find the...
Since
are solutions of the associated homogeneous equation, find the
general solution of the differential equation using the parameter
variation method. Write the system of equations and use Cramer's
rule to find the solution.
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(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
Please answer a. - e.
You are given a homogeneous system of first-order linear differential equations and two vector- valued functions, x(1) and x(2). <=(3 – )x;x") = (*), * x(2) (*)+-0) a. Show that the given functions are solutions of the given system of differential equations. b. Show that x = C1X(1) + czx(2) is also a solution of the given system for any values of cı and c2. c. Show that the given functions form a fundamental set...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem y'' = 0 : 1) the auxiliary equation is ar2 + br +c= = 0. 2) The roots of the auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = C1y1 + C2y2 for arbitrary constants ci and C2- Next...
2. [5pts] Given that y 1, e are solutions to the homogeneous version of the nonhomogeneous DE below, verify that they form a fundamental set of solutions. Then, use variation of parameters to find the general solution y(t)
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0: 1) the auxiliary equation is ar? + br +C = 242r42 = 0. 2) The roots of the auxiliary equation are 141-14 Center answers as a comma separated list). 3) A fundamental set of solutions is -1 .-1xco) Center answers as a comma separated list. Using these we obtain the the complementary solution y...
(10 pts) Find the general solution to the differential equation ty'+2y =t^3 What are the homogeneous solutions?
8. Solve the following first order homogeneous linear system of differential equations I a -B -B Cu = -3 4 -3 | u, 1-B –B a ) where a and B are real nonzero constants. Find a fundamental matrix and the inverse matrix of the fundamental matrix. Hint: dot1 TI 212/1 a 22).