Differential Equations Quiz

What is the first step in solving differential equations using separation of variables?

• Separate variables to different sides

• Solve for the constant of integration

• Apply implicit differentiation

• Integrate both sides immediately

What notation is used to represent the derivative in the separation of variables?

• Euler's notation

• Leibniz notation

• Lagrange's notation

• Newton's notation

After separating variables and integrating, what is added to both sides of the equation?

• A differential

• A variable of integration

• An exponent

• A constant of integration

What is the result of integrating 1 over y squared with respect to y?

• 1/(2y)

• ln|y|

• y^2/2

• -1/y

What is the antiderivative of sine x in the context of separation of variables?

• cosine x

• -cosine x

• tangent x

• secant x

Tags

CCSS.HSA-REI.B.4B

What mathematical operation is used to eliminate the reciprocal in an equation?

• Differentiation

• Integration

• Taking the reciprocal of both sides

• Multiplying by the derivative

Tags

CCSS.HSA.REI.A.1

In the context of differential equations, what does exponentiating both sides of an equation solve for?

• The constant of integration

• The variable y

• The integral of x

• The derivative dy/dx

What does the natural log function become when exponentiated?

• A new constant

• The variable y

• The constant e

• The original variable before taking the natural log

How is a constant treated when it is raised to the power of e in the context of solving differential equations?

• As an exponent

• As an unknown variable

• As a coefficient

• As a new variable

What is a common error when trying to separate variables in differential equations?

• Subtracting variables instead of dividing

• Adding instead of multiplying by dy/dx

• Incorrectly applying the chain rule

• Forgetting to add the constant of integration