Question

HW 07 - Homogeneous Equations with Constant Coefficients: Problenm Previous Problem Problem List Next Problem (1 point) Find the general solution to y ",-у', + 3y,-3y 0. In your answer, use cı, c2 and c3 to denote arbitrary constants and X the independent variable. Enter ci as c1, c2 as c2, and c3 as c3. help (equations)

Answer 1

The given differential equation is homogeneous linear difeediffere equation with constant cofficent.

For finding it's Sol ,we need to find the solution of corresponding auxiliary equations.

The whole process is given below ?

The given differential equation is homogeneous linear difference equation with constant coefficient. For finding it's Sol, we need to find the solution of corresponding auxiliary equations. The whole process is given below The given differential equation y tripleprime - y doubleprime + 3y' - 3y = 0 ---- (1) is a Homogeneous Linear Differential equation with constant coefficient. Here y is a function of x. And y' = dy/dx = Dy, Where D = d/dx. In operator notation (1) can be written as: (D^3 - D^2 + 3D - 3) y = 0 The Auxiliary equation is given as: - D^3 - D^2 + 3D - 3 = 0 D^2(D - 1) + 3(D - 1) = 0 (D^2 + 3) (D - 1) = 0 therefore D = 1, D = plusminus squareroot 3 i Hence The solution is given as y(x) = c_1e^x + c_2 cos squareroot 3 x + c_3 sin squareroot 3 x This is required solution.