(a) Find the general solution of the following second order linear differential equation given that y1 = t is known to be a solution:
t2y" - (t2 + 2t) y' + (t + 2)y = 0, t> 0.
(b) Find the particular solution given that y(1) = 7 and y'(1) = 4.
(a) Find the general solution of the following second order linear differential equation given that y1 = t is known to be a solution:
Find the general solution of the given second-order differential equation 3y" + y = 0 y(x) = _______
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) = _______
5) Consider the second order linear non-homogeneous differential equation tay" - 2y = 3t2 - 1,t> 0. a) Verify that y(t) = t- and y(t) = t-1 satisfy the associated homogeneous equation tay" - 2y = 0. (5 points) b) Find a particular solution to the non-homogeneous differential equation. (10 points) c) Find the general solution to the non-homogeneous differential equation. (5 points)
Find a second order linear equation L(y) = f(t) with constant coefficients whose general solution is: @ y=Cje24 + C261 + te3t @ (a) The solution contains three parts, so it must come from a nonhomogeneous equation. Using the two terms with undefined constant coefficients, find the characteristic equation for the homogeneous equation. (b) Using the characteristic equation find the homogeneous differential equation. This should be the L(y) we're looking for. (c) Since we have used two terms from the...
Find the general solution of the given second-order differential equation. y'' + 10y' + 25y = 0 Solve the given differential equation by undetermined coefficients. y'' + 4y = 2 sin 2x Solve the given differential equation by undetermined coefficients. y'' − y' = −10
Find the second order linear differential equation whose general solution is given by y=C1 cos4t + C2 sin4t -e^t sint
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). y'' + 2y' + y = 0; y1 = xe−x y2 =
Give a linear constant-coefficient differential equation that has general solution y(t) = e 2t + sin(2t) + c1e t + c2tet + c3e −t 7. Give a linear constant-coefficient differential equation that has general solution y(t) = {2+ + sin(2t) + let + Catet + cze-t
Find the general solution of the given second-order differential equation. 27"-3y + 4y = 0 Upload a completed solution of your work as a PDF, JPEG or DOCX file. Upload Choose a File Question 5 Find the general solution for the given second order differential equation. - 64+25 y = 0 Please show all work and upload a file (PDF, JPG, DOCX) of the work and circle your final answer. Upload Choose a File
Find the general solution of the following differential equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? + ?e^(-t). (please solve Question No.7 only) 7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...