Lesson H7
H7 Separable differential equations Quiz: AQA Maths, Unit 8
20 questions
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Lesson H7, Separable differential equations: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.
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The 20 questions
-
Which form is a separable first-order differential equation?
- dy/dx = f(x) g(y)
- d^2y/dx^2 = f(x)
- dy/dx = f(x) + g(y)
- dy/dx = x + y
-
What is the first step in solving dy/dx = xy by separation of variables?
- Differentiate both sides
- Divide by y and integrate both sides with respect to x
- Substitute y = x
- Multiply both sides by x
-
What is the general solution of dy/dx = ky for a constant k?
- y = Ae^(kx)
- y = kAe^x
- y = Ae^(x/k)
- y = Ax^k
-
Which expression results from solving y dy = x dx?
- y^2 = Cx^2
- y^2 - x^2 = C
- y = x + C
- y^2 + x^2 = C
-
Solve dy/dx = 2y with y = 3 when x = 0. Which expression gives y?
- y = 2e^(3x)
- y = e^(2x) + 3
- y = 3 + 2x
- y = 3e^(2x)
-
When solving a separable equation by dividing by y, what must be checked separately?
- Whether the gradient is positive
- The constant solution y = 0, which division by y can lose
- Whether x = 0 is a root
- The sign of the integration constant
-
Which is a general solution of dy/dx = 3x^2 y?
- y = Ae^(x^3)
- y = Ae^(x^2)
- y = Ax^3
- y = Ae^(3x^2)
-
Which is a general solution of dy/dx = y/x?
- y = Ax
- y = A ln x
- y = A/x
- y = Ae^x
-
Solve dy/dx = x/(2y) with y = 2 when x = 0. Which expression gives y in terms of x?
- y^2 = x^2 + 4
- y^2 = x^2/2 + 4
- y^2 = 4x^2 + 4
- y = x^2/4 + 2
-
A particle has dv/dt = -2v with v = 10 when t = 0. Which expression gives v?
- v = 10 - 2t
- v = 10e^(-2t)
- v = 5e^(-2t)
- v = -2e^(10t)
-
Demand satisfies dQ/dp = -0.1Q with Q = 200 when p = 0. Approximately what is Q when p = 10?
- 74
- 100
- 37
- 121
-
Solve dy/dx = x(1 + y) with a general constant A. Which expression gives y?
- y = x^2/2 + A - 1
- y = Ae^(x^2) - 1
- y = Ae^(x^2/2) + 1
- y = Ae^(x^2/2) - 1
-
Solve dy/dx = 2x(y - 1) with y = 3 when x = 0. Which expression gives y?
- y = 2 + e^(2x)
- y = 1 + 3e^(x^2)
- y = 2 + e^(x^2)
- y = 1 + 2e^(x^2)
-
Solve dy/dx = x y^2 with y = 1 when x = 0. Which expression gives y?
- y = 2/(2 - x^2)
- y = 2/(2 + x^2)
- y = 1/(1 - x^2)
- y = 1/(1 + x^2/2)
-
Solve dy/dx = 3y/(x + 1). Which is the general solution?
- y = A(x + 1)^3
- y = 3A(x + 1)
- y = A(x + 1)/3
- y = Ae^(3x + 1)
-
Solve dy/dx = x e^(-y). Which expression gives y in terms of x?
- y = ln(x^2/2 + C)
- y = e^(x^2/2) + C
- y = x^2/2 + ln C
- y = -ln(x^2/2 + C)
-
A resisted motion satisfies dv/dt = -kv^2 with v = v0 at t = 0. Which expression gives v?
- v = v0/(1 + k v0 t)
- v = v0 e^(-kt)
- v = v0/(1 - kt)
- v = v0 - kt^2
-
Solve dy/dx = -y^2 with y = 2 when x = 0. Which expression gives y?
- y = 2/(1 + 2x)
- y = 2/(1 - 2x)
- y = 2e^(-x)
- y = 1/(2 + x)
-
Which is the general solution of y dy/dx = e^x?
- y^2 = e^x + A
- y = 2e^x + A
- y = e^x + A
- y^2 = 2e^x + A
-
Solve dy/dx = 4x/y with y = 2 when x = 0. Which expression gives y^2 in terms of x?
- y^2 = 4x^2 - 4
- y^2 = 4x^2 + 4
- y = 2x^2 + 2
- y^2 = 2x^2 + 4
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