Lesson 9.5-9.7
9.5-9.7 Second order differential equations Quiz: Pearson Edexcel Further Maths, Unit 9
20 questions
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Lesson 9.5-9.7, Second order differential equations: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 9: Differential equations, written with Revision Ninja.
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The 20 questions
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What is the general solution of y'' - 3y' + 2y = 0?
- y = A e^x + B e^(2x)
- y = (A + Bx) e^x
- y = A cos x + B sin x
- y = A e^(-x) + B e^(-2x)
-
What is the general solution of y'' + 4y = 0?
- y = A e^(2x) + B e^(-2x)
- y = (A + Bx) e^(2x)
- y = A cos 2x + B sin 2x
- y = A cos 4x + B sin 4x
-
What is the general solution of y'' - 4y' + 4y = 0?
- y = A e^(2x) + B e^(-2x)
- y = e^(2x)(A cos 2x + B sin 2x)
- y = A e^(4x) + Bx
- y = (A + Bx) e^(2x)
-
What is the general solution of y'' + 2y' + 5y = 0?
- y = e^(-x)(A cos 2x + B sin 2x)
- y = e^(-x)(A cos 5x + B sin 5x)
- y = A e^(-5x) + B e^x
- y = e^(2x)(A cos x + B sin x)
-
For y'' + y = 3, what is a particular integral?
- y = (3/2) x^2
- y = 3
- y = 3x
- y = 3 e^x
-
For y'' - y = e^(2x), what is a particular integral?
- y = 2e^(2x)
- y = e^(2x)
- y = e^(2x)/4
- y = e^(2x)/3
-
What condition on a and b in y'' + ay' + by = 0 gives oscillatory solutions?
- a^2 = 4b
- a^2 < 4b
- a < 0
- a^2 > 4b
-
Find the period of simple harmonic motion with x'' = -4x.
- 4 pi
- pi
- 2 pi
- pi/2
-
Find the period of simple harmonic motion with x'' = -9x.
- 3 pi/2
- 2 pi/3
- 2 pi/9
- pi/3
-
Solve y'' - 2y' + y = 0 with y(0) = 1 and y'(0) = 2.
- y = (1 + 2x) e^x
- y = e^x + 2x
- y = (1 + x) e^x
- y = (1 + x) e^(-x)
-
Solve y'' + 2y' + 2y = 0 with y(0) = 0 and y'(0) = 1.
- y = e^(-2x) sin x
- y = e^(-x) cos x
- y = e^(-x) sin x
- y = e^x sin x
-
Solve y'' + y = 0 with y(0) = 1 and y'(0) = 0.
- y = sin x
- y = 1 + x
- y = e^x
- y = cos x
-
What is the general solution of y'' + 3y = 0?
- y = A e^(sqrt 3 x) + B e^(-sqrt 3 x)
- y = (A + Bx) e^(sqrt 3 x)
- y = A cos(sqrt 3 x) + B sin(sqrt 3 x)
- y = A cos(3x) + B sin(3x)
-
For y'' + y' = x, which polynomial form is a particular integral?
- y = x^2/2 + x
- y = x/2
- y = x^2/2 - x
- y = x^2 + x
-
What is the general solution of y'' + 6y' + 9y = 0?
- y = (A + Bx) e^(-3x)
- y = e^(-3x)(A cos 3x + B sin 3x)
- y = A e^(-3x) + B e^(3x)
- y = A e^(-9x) + B
-
Solve y'' + 4y = 0 with y(0) = 0 and y'(0) = 2.
- y = 2 cos 2x
- y = 2 sin 2x
- y = sin x
- y = sin 2x
-
What is the general solution of y'' - y' - 6y = 0?
- y = A e^(3x) + B e^(-2x)
- y = A cos 3x + B sin 2x
- y = A e^(-3x) + B e^(2x)
- y = (A + Bx) e^(3x)
-
What is the general solution of y'' + 4y' + 13y = 0?
- y = e^(-2x)(A cos 13x + B sin 13x)
- y = A e^(-2x) + B e^(-3x)
- y = e^(-2x)(A cos 3x + B sin 3x)
- y = e^(-4x)(A cos 13x + B sin 13x)
-
What is the complementary function of y'' - 5y' + 6y = 0?
- A e^(-2x) + B e^(-3x)
- A cos 2x + B sin 3x
- A e^(2x) + B x e^(3x)
- A e^(2x) + B e^(3x)
-
If the discriminant of the auxiliary equation is zero, what form does the general solution take?
- A e^(m1 x) + B e^(m2 x), two distinct real roots
- e^(px)(A cos qx + B sin qx), complex roots
- No solution exists
- (A + Bx) e^(mx), a repeated real root
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