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Question 5 (20 points) Solve the following IVP: (y + y - 2y = 4.2 y(0)...
) For the IVP y+2y-2-e(0)- Use Euler's Method with a step size of h 5 to find approximate values of the solution at t-1 Compare them to the exact values of the solution at these points.
completeness and clarity 2. Find a particular solution for the IVP y" - 2y + 2y = 8(t - 5), y(0) = 0, y0) = 1
1) Solve the following ODE with IVP 2y" + 6y' - 8y = 0 y(0) = 4 y'(0) = -1
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
Question 2 Given the following second order IVP: y" – 2y' + y = e*, y(0) = 0, y'(0) = 1. 1. Solve it using the undetermined coefficients method. [2 pt] 2. Solve it again using the Laplace Transform. (2.5 pt] 3. Which method did you find easier and why? [0.5 pt]
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
(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...
13) (15 pts) Solve the given IVP. y" + 2y' + 2y = 10 sin(2t), y(0) = 1, y'(0) = 0
Find the first five terms of the series solution to the IVP (y +(1-2) +2y=e", y(0) = -5, (y0 =1, by making use of the general power series representation in (2). Hint: Recall the Taylor/power series for et about the point 0.
help me 1 Solve the egua rim : y" - 2y' + 2y 0• (20) 2 Solve the equotion: y" - 4y' + 5y = 0 y(0) = 2 y'(0)= 6 • (20) 3 Solve the linear system: (20) X, +2x2 + 3x, = 7 2x, + 5x, + 3x3 = 12, %3D X1+ 0x2 + 8x3 = 10 4 Pind the eigenvəlues, and eiyenvectors (20) 4 -1 5 Find the relation ship between x and y. (20) Y=ax+b, a=?,...