Lesson I4-I6
I4-I6 Second order linear equations Quiz: AQA Further Maths, Unit 2
20 questions
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Lesson I4-I6, Second order linear equations: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.
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The 20 questions
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What is the auxiliary equation of y'' + a y' + b y = 0?
- m^2 + a + b = 0
- m^2 - a m + b = 0
- m^2 + a m + b = 0
- m^2 + a m - b = 0
-
If the auxiliary equation discriminant is positive, what type of roots exist?
- Repeated real
- Two distinct real
- Complex conjugate
- Pure imaginary
-
If the discriminant of the auxiliary equation is zero, what is the form of the general solution?
- (A + Bx) e^(mx)
- A e^(m1 x) + B e^(m2 x)
- e^(px)(A cos(qx) + B sin(qx))
- A + Bx
-
If the auxiliary equation has complex roots p +/- qi, what is the general solution?
- e^(px)(A cos(qx) + B sin(qx))
- A e^(px) + B e^(-px)
- (A + Bx) e^(px)
- e^(qx)(A cos(px) + B sin(px))
-
What is the general solution of the homogeneous differential equation called?
- General solution
- Integrating factor
- Complementary function
- Particular integral
-
How is the general solution of a non-homogeneous linear differential equation formed?
- CF + PI
- CF × PI
- CF - PI
- PI - CF
-
Find the general solution of y'' - 3y' + 2y = 0.
- y = (A + Bx) e^x
- y = A cos x + B sin x
- y = A e^(-x) + B e^(-2x)
- y = A e^x + B e^(2x)
-
Find the general solution of y'' + 4y' + 4y = 0.
- y = e^(-2x)(A cos(2x) + B sin(2x))
- y = A e^(-2x) + B e^(2x)
- y = (A + Bx) e^(2x)
- y = (A + Bx) e^(-2x)
-
Find the general solution of y'' + 2y' + 5y = 0.
- y = e^(-x)(A cos(2x) + B sin(2x))
- y = e^(x)(A cos(2x) + B sin(2x))
- y = e^(-2x)(A cos(x) + B sin(x))
- y = A e^(-x) + B e^(-5x)
-
A particular integral of y'' - y = 2x is which function?
- y = 2x
- y = -2x
- y = -2
- y = x^2
-
A particular integral of y'' + y = e^x is which function?
- y = 2 e^x
- y = e^x / 3
- y = e^x
- y = (1/2) e^x
-
Solve y'' + 2y' + y = 0 with y(0) = 1 and y'(0) = 0.
- y = (1 + 2x) e^(-x)
- y = e^(-x)
- y = (1 - x) e^(-x)
- y = (1 + x) e^(-x)
-
A particular integral of y'' - 2y' = 4 is which function?
- y = -4x
- y = -2
- y = 2x
- y = -2x
-
Find the particular integral of y'' - 4y' + 4y = 8.
- y = 2x
- y = 8
- y = -2
- y = 2
-
What type of roots does the auxiliary equation of y'' + 6y' + 9y = 0 have?
- One repeated root
- No real roots
- Complex conjugate roots
- Two distinct roots
-
Find the general solution of y'' - 2y' + 5y = 0.
- y = A e^x + B e^(5x)
- y = e^x(A cos(x) + B sin(x))
- y = e^(2x)(A cos(x) + B sin(x))
- y = e^x(A cos(2x) + B sin(2x))
-
Find a particular integral of y'' + 3y' + 2y = e^(-x).
- x e^(-x)
- -x e^(-x)
- e^(-x)
- 2x e^(-x)
-
Solve y'' - 5y' + 6y = 0 with y(0) = 2 and y'(0) = 5.
- y = e^(2x) + 2 e^(3x)
- y = e^(-2x) + e^(-3x)
- y = 2 e^(2x) + e^(3x)
- y = e^(2x) + e^(3x)
-
Find a particular integral of y'' + y' - 2y = x.
- y = x/2 + 1/4
- y = -x/2 - 1/4
- y = -x/2 + 1/4
- y = -x/2
-
Which second order equation has general solution y = A e^(2x) + B x e^(2x)?
- y'' - 4y = 0
- y'' - 4y' + 4y = 0
- y'' + 4y' + 4y = 0
- y'' - 2y' + 4y = 0
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