Practice General Form (1.4.1) - Linear Differential Equations - Mathematics (Civil Engineering -1)

Practice: General Form

Lesson 1.4.1Linear Differential Equations

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the general form of a second-order linear differential equation?
Show hintHide hint
Look for the highest derivative present in the equation.
Question 2.
Define a homogeneous differential equation.
Show hintHide hint
What happens to the non-homogeneous part?
3Question 3.
What is the standard form of a second-order linear differential equation?
- $$\\frac{d^2y}{dx^2} + P(x) \\frac{dy}{dx} + Q(x)y = R(x)$$
- $$\\frac{dy}{dx} + P(y) = R(x)$$
- $$\\frac{d^2y}{dx^2} + Q(x) = 0$$
Show hintHide hint
Look for the order of the derivatives present.
4Question 4.
Which type of equation is represented by $R(x) = 0$ ?
- True
- False
Show hintHide hint
Remember what makes an equation homogeneous.
Question 5.
For the differential equation $\frac{d^2y}{dx^2} + 5y = 0$ , find the auxiliary equation and classify its solutions based on the roots.
Show hintHide hint
What form does the solution take when roots are complex?
Question 6.
Given the non-homogeneous equation $\frac{d^2y}{dx^2} - y = e^{2x}$ , identify the general solution and the particular solution.
Show hintHide hint
What’s your strategy for handling the right side of the equation?

5 more questions in this section. Enroll free to practise them all.