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2542261
FP3 differential equations
Description
First order linear Second order linear Solving through substitution
No tags specified
fp3
maths
further maths
a level
Quiz by
Joseph Stevens
, updated more than 1 year ago
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Created by
Joseph Stevens
over 9 years ago
21
1
0
Resource summary
Question 1
Question
Find the integrating factor for which
Image:
b0208d29-4130-41b2-8761-01e54672517d (image/png)
Answer
sin x
cot x
cosec^2 x
ln|cot x|
Question 2
Question
Hense solve.
Image:
42fe3e90-2fd8-42cd-8403-59c379226c49 (image/png)
Answer
y= cos x + cot x ln|sinx| + c
y = tan x + ln|cot x|
y = cosec x + cot x ln|cot(x/2)|+ c
y=sin x - tan x ln|tan(x/2)| + c
Question 3
Question
Find the complimentry function of the following differential equation.
Image:
bb2e67b9-4c65-4331-8b68-21e21603c0de (image/png)
Answer
y=e^-2x (Acos √3x + Bsin √3x)
y= Ae^2x +Bie^3x
y= Ae^√3ix + Bcos 2x
y= e^4x +A
Question 4
Question
Find the particular integral.
Image:
138e1b4e-6eb8-42cd-a4a4-bc85f3610e4e (image/png)
Answer
y= 4e^-x + 6sin x + 4cos x
y= e^-2x (Acos √3x + Bsin √3x)
y=(3/4)e^-x + (6/5) sin x - (4/5) cos x
y = e^x + 4sin x + 7cos x
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