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is the solution of this given problem . If you are satisfied plz do
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Y13) = re-1+21)22 42(2) = zel-1-21)22 Write the solution yı (2) as a sum of real...
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...
a) Find the real part u(x,y) and imaginary part v(x,y) of f(2)= (1+2i )z? + (i – 1)2 +3 b) Verify if the above function is analytic c) Using Laplace's equation verify if the real part u(x,y) is harmonic.
(1 point) 2 a. Find the most general real-valued solution to the linear system of differential equations a' -4 -8 21(t) ] =C1 + C2 22(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these preview answers
prove that J2(x)=sum from k=0 to infinity [
(-1)^k/2^9@k+2)*k!(k+2)! ]*x^(2k+2) is a solution of the Bessel
differential equation of order 2:
x^2y'' + xy' + (x^2-4)y=0
(-1)4 9- Using the ratio test, one can easily show that the series +2converges for all e R. Prove that (-1)X h(x) = E, 22k +2k!(k + 2)! 22+2 is a solution of the Bessel differential equation of order 2: In(x) is called the Bessel function of the first Remark. In general the function...
Please write clear in the explanation thanks
1 2 0 -1 3 2 1 -1 2 1 oand RREF(A)- 1 3 -1 2 Suppose that A3 21 a. s there a unique solution to Ax-22 Justify your reasoning completely ?Justify your reasoning completely. b. Are the column vectors of A a basis for R? Justify your reasoning. c. Define geometrically the span of A.
1 2 0 -1 3 2 1 -1 2 1 oand RREF(A)- 1 3 -1 2...
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(a) Show that an members of the family y-ve-1ฐ are-lutkn-ed Medaterntial mpalii (b) Use part (a) to find a fornvula for the solution to the ini- tial value problem v (0)-2. Then, sketch your solution on the slope field shown to the right. 2. Figure 1. Slope field for 3. (a) Show that all members of the family yarlutions of the disferential equation (b) Find the solution to the initial value problem ry'-tra-Zy·y(1)-S. 4. For what...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
1.) solve the problem y'=(x+1)y yo) =1 numencally for 4 (02) using hol? 2 1:21 A B 1.2 E).221 2.) y - 4y + 4y =0 A. Y = e Y2 = Xe x A Two linearly independent Solutions of the differenthal equation are? B. Y =é 3x Cirl =é D. Yl=eax E, Y = ex 1 Y 2 =Xex + Y2 = Xerzy 42=e-2x Y = e zx + 3.) The radius of convergence of the Power Senes x/n...