3. First-Order Equations II

Integrating Factors — Quiz

Test your understanding of integrating factors with 5 practice questions.

Practice Questions

Question 1

For a linear first-order differential equation of the form $y'+P(x)y=Q(x)$, what is the integrating factor?

Question 2

Find the integrating factor for the differential equation $y'+3y=e^x$.

Question 3

After multiplying $y'+2y=4$ by the integrating factor $e^{2x}$, what is the left side rewritten as?

Question 4

Solve the initial value problem $y'+y=2$ with $y(0)=1$.

Question 5

Solve the differential equation $y'+\frac{2}{x}y=x$ for $x>0$.