Directly quoted:
Consider the differential equation:
y" = -3y' - 2y -et
i) What sort of differential equation is this?
ii) What is yh(t), the general homogeneous solution?
iii) What is yp(t), the particular inhomogeneous solution?
iv) If y(0) = 0 and y(ln(2)) = 1, what is the full specific solution?
So far I have gotten:
Second Order Linear inhomogeneous differential equation
y" + 3y' + 2y = 0
<L = Lambda>
L 2 + 3L + 2 = 0
(L + 2)(L + 1) L = -2, -1
Yn(t) = c1 e-2t + c2 e-t
y" + 3y' +2y = -et
y(t) = aect
y'(t) = acect
y"(t) = ac2ect
C = 1
a(1)2et + 3a(1)et + 2aet = -et
aet + 3aet + 2aet = -et
aet + 5aet + 2aet = -et
6aet = -et 6a = -1 a = -1/6
...and because I could see that this didn't make sense I just stopped. Can someone help me understand where I got off track and how I should have proceeded?
Consider the differential equation:
y" = -3y' - 2y -et
i) What sort of differential equation is this?
ii) What is yh(t), the general homogeneous solution?
iii) What is yp(t), the particular inhomogeneous solution?
iv) If y(0) = 0 and y(ln(2)) = 1, what is the full specific solution?
So far I have gotten:
Second Order Linear inhomogeneous differential equation
y" + 3y' + 2y = 0
<L = Lambda>
L 2 + 3L + 2 = 0
(L + 2)(L + 1) L = -2, -1
Yn(t) = c1 e-2t + c2 e-t
y" + 3y' +2y = -et
y(t) = aect
y'(t) = acect
y"(t) = ac2ect
C = 1
a(1)2et + 3a(1)et + 2aet = -et
aet + 3aet + 2aet = -et
aet + 5aet + 2aet = -et
6aet = -et 6a = -1 a = -1/6
...and because I could see that this didn't make sense I just stopped. Can someone help me understand where I got off track and how I should have proceeded?