Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify P, Q, and R in the equation ∂z/∂x + 2∂z/∂y = 3z.
💡 Hint: Express the PDE in the standard form Pp + Qq = R.
Question 2
Easy
What is the general form of a first-order PDE?
💡 Hint: Recall the elements of the equation.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the form of Lagrange's Linear Equation?
- Pp + Qq = 0
- Pp + Qq = R
- ∂z/∂x + ∂z/∂y = z
💡 Hint: Remember the equation form we discussed in class.
Question 2
Auxiliary equations arise from what kind of transformations?
- True
- False
💡 Hint: Think about how we derived them in examples.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the PDE ∂z/∂x + ∂z/∂y = 5, use Lagrange's method to find the general solution and explain the steps.
💡 Hint: Pay attention to the integration steps and constants involved.
Question 2
For the equation ∂z/∂x + (sqrt(x) + 1)∂z/∂y = 0, derive the general solution using Lagrange's characteristics.
💡 Hint: Notice how sqrt(x) influences the auxiliary equation structure.
Challenge and get performance evaluation