y′′+y′−2y=6sin(x)
is called a differential equation because it involves an unknown
function y=f(x)y=f(x) and its derivatives y′y′ and y′′y″.
Find constants AA and BB such that the function
y=Asin(x)+Bcos(x)y=Asin(x)+Bcos(x) satisfies this equation.
A=
B=
y′′+y′−2y=6sin(x) is called a differential equation because it involves an unknown function y=f(x)y=f(x) and its derivatives...
2. [3 marks] Consider the function f(x,y) = log (– 2y). (a) Find the partial derivatives (b) Find an equation of the tangent (plane) to the surface of f at the point (3,1, f (3,1)).
2. Given the nonhomogeneous 2nd order differential equation y" +2y = xe*: (8 pts) a. Identify the forcing function (ie. the nonhomogeneous term we call f(x)). b. Write the homogeneous equation associated with this DE. c. Find the particular solution to the homogeneous DE from part b which satisfies the initial conditions y(0) = 2, y'(O)=-1. (note: you will NOT be using technique of undetermined coefficients)
Verify that the given function is a solution to the given differential equation (c1 and c2 are arbitrary constants) and state the maximum interval over which the solution is valid. For Problems 7-21, verify that the given function is a solu- tion to the given differential equation (cy and c2 are arbitrary constants), and state the maximum interval over which the solution is valid. ya Sx +42 25 WID#cigos x A Asin 2%, = 0 BAWK vel Hope 2y +10....
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =
hellllllllllp please a) Verify that the function y = ?? + is a solution of the differential equation zy' +2y 4x? (x > 0). b) Find the value ofe for which the solution satisfies the initial condition (2) - 5. = Submit Question a) Verify that the function y=x? + с 2 is a solution of the differential equation ry' + 2y = 4x², (x > 0). b) Find the value of c for which the solution satisfies the initial...
Determine if the given function y- f(x) is a solution of the accompanying differential equation Differential equation: 9xy' + 9y-cos x Initial condition: y()0 Solution candidate: y- x O a. No b. Yes Determine if the given function y- f(x) is a solution of the accompanying differential equation Differential equation: 9xy' + 9y-cos x Initial condition: y()0 Solution candidate: y- x O a. No b. Yes
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
Find the function y = y(2) (for x > 0) which satisfies the separable differential equation dy 6 + 14.2 dic 12 2 0 with the initial condition y(1) = 3. y=
QUESTION 11 Question: A function y(x) satisfies the differential equation ay" +ay', + ају +aoy 54.6 xe 3 and the stated differential equation has charac- y(x) teristic polynomial pr) 3r-23r+ 1). Then the value of lim (A) 0.409721 (B) 0.270431 (C) 0.272703 (D) 0.0769268 (E) 0.337037 (F) 0.379485 (G) 0.0311248 (H) 0.21498 1S -900 QUESTION 11 Question: A function y(x) satisfies the differential equation ay" +ay', + ају +aoy 54.6 xe 3 and the stated differential equation has charac- y(x)...
The function Y(t) = t is a solution of the differential equation (t2+4)y" - 2ty' + 2y = 0. Find a real general solution of this equation.