Lesson I1-I3
I1-I3 First order equations with integrating factors and modelling Quiz: AQA Further Maths, Unit 2
20 questions
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Lesson I1-I3, First order equations with integrating factors and modelling: 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
-
For the first order equation dy/dx + P(x) y = Q(x), what is the integrating factor?
- e^(integral of P(x) dx)
- e^(-integral of P(x) dx)
- e^(integral of Q(x) dx)
- integral of P(x) dx
-
Multiplying dy/dx + P(x) y = Q(x) by an integrating factor I(x) gives which equation?
- I dy/dx = Q
- d/dx (I y) = Q
- d/dx (y) = I Q
- d/dx (I y) = I Q
-
How many arbitrary constants are in the general solution of a first-order differential equation?
- One
- Zero
- Two
- Infinitely many
-
What is used to find the arbitrary constant in a general solution?
- Auxiliary equation
- Initial condition
- Particular integral
- Integrating factor
-
What is the integrating factor for dy/dx - 3y = x?
- e^(-3x)
- -3 e^(-3x)
- e^x
- e^(3x)
-
Which equation is a first order linear differential equation?
- dy/dx + y^2 = x
- d^2y/dx^2 + y = 0
- dy/dx + 3xy = sin(x)
- y dy/dx = x
-
The integrating factor method solves differential equations of which order and type?
- Second-order non-linear
- First-order linear
- First-order non-linear
- Second-order linear
-
Solve dy/dx + y = e^x with y(0) = 0.
- y = e^x / 2
- y = e^x - e^(-x)
- y = sinh(x)
- y = cosh(x)
-
Find the general solution of dy/dx - 2y = 1.
- y = C e^(2x) + 1/2
- y = C e^(-2x) - 1/2
- y = C e^(2x) - 1/2
- y = C e^(2x) - 1
-
Find the general solution of dy/dx + 2xy = 2x.
- y = 2 + C e^(-x^2)
- y = x + C e^(-x^2)
- y = 1 + C e^(-x^2)
- y = 1 + C e^(x^2)
-
A particle has dv/dt + v/5 = 10 with v(0) = 0. Which expression gives v in terms of t?
- v = 50(1 - e^(-t/5))
- v = 10(1 - e^(-t/5))
- v = 50 e^(-t/5)
- v = 50(1 - e^(t/5))
-
In the model dv/dt + v/5 = 10 with v(0) = 0, what is the limiting value of v as t tends to infinity?
- 10
- 0
- 5
- 50
-
Find the general solution of dy/dx + 2y/x = 4x for x > 0.
- y = x + C/x^2
- y = x^2 + C/x^2
- y = 2x^2 + C/x^2
- y = x^2 + C/x
-
Solve dy/dx + y = 0 with y(0) = 3.
- y = -3 e^(-x)
- y = 3 - x
- y = 3 e^(-x)
- y = 3 e^x
-
Find the general solution of dy/dx + y = x.
- y = x - 1 + C e^(-x)
- y = x + C e^(-x)
- y = x - 1 + C e^x
- y = x + 1 + C e^(-x)
-
Find the general solution of dy/dx + y/x = x^2 for x > 0.
- y = x^3/4 + C/x
- y = x^3/4 + C
- y = x^3/3 + C/x
- y = x^2/4 + C/x
-
Find the particular solution of dy/dx + 2y = 4 with y(0) = 3.
- y = 3 e^(-2x)
- y = 4 + e^(-2x)
- y = 2 - e^(-2x)
- y = 2 + e^(-2x)
-
What is the integrating factor for dy/dx + (2/x) y = sin(x) when x > 0?
- 2x
- e^(2x)
- x^2
- 1/x^2
-
For dy/dx + y tan(x) = sec(x), find the general solution for -pi/2 < x < pi/2.
- y = sin(x) + C sec(x)
- y = cos(x) + C sin(x)
- y = tan(x) + C cos(x)
- y = sin(x) + C cos(x)
-
Solve dy/dx = 2y with y(0) = 4.
- y = 4x e^(2x)
- y = 4 e^(2x)
- y = 2 e^(4x)
- y = 4 e^(-2x)
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