16.7 - Solution of First-Order Linear PDE – Lagrange’s Method
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the general form of a first-order linear PDE?
💡 Hint: Look for the derivatives involved in the equation.
Explain what auxiliary equations are.
💡 Hint: Think about how they relate to the original PDE.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What technique is used to solve first-order linear PDEs?
💡 Hint: Recall the discussion on PDE solutions.
Are auxiliary equations integral to finding solutions in Lagrange's method?
💡 Hint: Think about how we formed our auxiliary equations.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Solve the PDE ∂z/∂x + 2∂z/∂y = e^x and find the general solution.
💡 Hint: Make sure to isolate variables during integration!
Discuss how boundary conditions affect the solutions derived via Lagrange’s method.
💡 Hint: Consider how they adjust the constants in your general solution.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.