2. Find the general solution of the Euler's equation ty" - 3ty' + 3y = 0...
ters) SUIVe y + y - Sez. Find the general solution to ty" + 3ty' +y = 0 given that yı = t-1 is one solution. 1x , ,- 8+ (0) - 1 10 _1
(3) Consider the differential equation ty' + 3ty + y = 0, 1 > 0. (a) Check that y(t) = 1-1 is a solution to this equation. (b) Find another solution (t) such that yı(t) and (t) are linearly independent (that is, wit) and y(t) form a fundamental set of solutions for the differential equation).
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
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) = _______
Find the general solution to the differential equation: ty'+2y =t3, and what are the homogenous solutions. Find the general solution to the differential equation: ty'+2y = 3
7. Consider the first order differential equation 2y + 3y = 0. (a) Find the general solution to the first order differential equation using either separation of variables or an integrating factor. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem 2y + 3y = 0, y(0) = 4.
(15 pts) Find the general solution of the following equation. y" +5y"+ 3y - 9y 0. (Hint: Rational root test)
Q2: Find a general solution to the differential equation 3y" (e)3y(e) csc3 (e) SC = Q2: Find a general solution to the differential equation 3y" (e)3y(e) csc3 (e) SC =
1. Consider the following differential equation. ag = ty, y(0)=1. dt (a) Use Euler's Method with At = .1 to approximate y(1). (b) Use Euler's Method with At = .05 to approximate y(1). (c) Find the exact solution to the problem. Use this solution to compare the error for the different values of At. What does this say about the method? Note: On the course page there are notes describing an implementation of Euler's method on a spread sheet.
(10 pts) Find the general solution to the differential equation ty'+2y =t^3 What are the homogeneous solutions?