Separable First-Order Differential Equations Quiz

What is the first step in solving the differential equation dy/dx = x * y^2?

• Add x to both sides

• Move dx to the other side

• Multiply both sides by y^2

• Subtract y^2 from both sides

After separating variables in dy/dx = x * y^2, what is the next step?

• Differentiate both sides

• Integrate both sides

• Multiply both sides by x

• Divide both sides by y

In the equation dy/dx = sin(x)/y, what is the result of separating variables?

• y dy = sin(x) dx

• dy = y sin(x) dx

• dy = sin(x) dx

• dy = dx/y

What is the antiderivative of sin(x) with respect to x?

• -sin(x)

• -cos(x)

• cos(x)

• sin(x)

How do you separate variables in the equation dy/dx = e^(x-y)?

• Multiply both sides by e^y

• Add e^y to both sides

• Divide both sides by e^x

• Subtract e^x from both sides

What is the antiderivative of e^y with respect to y?

• e^y

• y * e^y

• 1/y

• ln(y)

Why is it difficult to solve for y in the equation 1/x^3 * y' = 1/(1-y^2)?

• The integration is not possible

• The equation is not separable

• The variables cannot be separated

• The resulting equation is complex

What is the first step in solving x * dy/dx = xy + x + y + 1?

• Factor out common terms

• Add x to both sides

• Divide both sides by x

• Multiply both sides by y

In the equation x * dy/dx = xy + x + y + 1, what common factor can be factored out?

• 1

• x

• y

• x + y

What is the final form of y in the equation x * dy/dx = xy + x + y + 1 after solving?

• y = e^x - x

• y = x * e^x - 1

• y = e^x + x

• y = x * e^x + 1