6) a) Find the general solution to the 2nd order
differential equation
y''+6y'+8y=0
[8 pts]
b) Find the general solution to
y''+6y'+8y=2e-x.
Use the method of undetermined coefficients. [8
pts]
c) Solve the IVP
y''+6y'+8y=2e-x,
y0=0,
y'0=0
[5 pts]
x2 y" + (x2+x) y’
+(2x-1) y = 0,
Find the general solution of y1 with
r1 and calculate the coefficient up to
c4 and also find the general expression of the
recursion formula, (recursion formula for
y1)
Find the general solution of y2 based on
theorem 4.3.1. (Hint, set d2 = 0)
1. Find the solution of y" + 8y' = 896sin(8t) + 256cos(8t)
with y(0) = 9 and y'(0) = 9
y = ?
2. Find y as a function of x if y"' - 9y" + 18y' = 20e^x ,
y(0) = 30 , y'(0) = 23 , y"(0) = 17
y(x) = ?
Consider the equation y''− (sin x)y = 0.
Find the general solution as a power series centered at x = 0.
Write the first six nonzero terms of the solution. Write the two
linearly independent solutions that form the general solution.
Differential Equations