Differential Equations Concepts Review

What is the correct form of a linear first order differential equation?

• dy/dt - P(t) * y = F(t)

• dy/dt + P(t) * y = F(t)

• dy/dt = P(t) * y + F(t)

• dy/dt + y = P(t) * F(t)

In the given equation, what is the value of P(t)?

• 2

• 3

• 5

• 4

How is the integrating factor μ(t) determined?

• By calculating e raised to the integral of P(t)

• By differentiating P(t)

• By integrating F(t)

• By multiplying P(t) and F(t)

What is the purpose of multiplying the differential equation by the integrating factor?

• To eliminate the constant term

• To transform the equation into a derivative of a product

• To simplify the equation

• To find the value of y

Which rule is applied to check the derivative of the product on the left side?

• Product rule

• Quotient rule

• Power rule

• Chain rule

What method is used to evaluate the integral on the right side of the equation?

• Integration by parts

• Trigonometric substitution

• Partial fractions

• Substitution

What is the first step in integration by parts?

• Multiply U and V

• Choose U and differentiate it

• Integrate U

• Differentiate V

How do you handle the constant of integration when determining μ(t)?

• Add it to both sides

• Subtract it from both sides

• Ignore it

• Include it in the final solution

What is the final step to find the general solution of the differential equation?

• Multiply both sides by e^4T

• Divide both sides by e^4T

• Add a constant to both sides

• Subtract a constant from both sides

What does the general solution of the differential equation include?

• A constant term

• All of the above

• An exponential decay term

• A trigonometric function