
Separable Differential Equations Concepts

Interactive Video
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Mathematics
•
9th - 12th Grade
•
Hard

Lucas Foster
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a separable differential equation?
An equation that cannot be integrated.
An equation that involves only one variable.
An equation that can be expressed as g(y) dy = f(x) dx.
An equation that can be written as a product of two functions.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example given, what is the first step after identifying the equation as separable?
Add a constant to both sides.
Cross-multiply to separate variables.
Multiply both sides by dx.
Differentiate both sides.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating 15y^4 dy?
3y^5 + C
5y^3 + C
y^5 + C
15y^5 + C
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the constant C when given a boundary condition?
By setting y and x to zero in the general solution.
By integrating the general solution.
By multiplying the general solution by a constant.
By differentiating the general solution.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the explicit particular solution when y = 0 and x = 0?
y = (x - cos(x) + 1)^(1/5) / 3
y = (x + cos(x) + 1)^(1/5) / 3
y = (x - sin(x) + 1)^(1/5) / 3
y = (x - cos(x) - 1)^(1/5) / 3
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the advantage of using definite integrals in solving DEs with boundary conditions?
It eliminates the need for algebraic manipulation.
It provides a numerical solution.
It avoids the need for integration.
It automatically satisfies the boundary condition.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When is using definite integrals not applicable?
When the DE is linear.
When the DE is not separable.
When the DE involves trigonometric functions.
When the boundary condition is complex.
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