Solve the equation in one-dimension subject to the boundary condition $d^2V/dx^2 = b$ where b is a constant V(x = 0) = 0 and V(x = L) = 2$\phi_0$
Added by Michael S.
Close
Step 1
Integrating once, we have: dV/dx = bx + c1 Integrating again, we have: V(x) = (b/2)x^2 + c1x + c2 Now, let's use the boundary conditions to find the values of the constants c1 and c2. From the condition V(x = 0) = 0, we have: V(0) = (b/2)(0)^2 + c1(0) + c2 = Show more…
Show all steps
Your feedback will help us improve your experience
Rajendra Kumar and 63 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Given the following boundary value problem 0.01 T - d^2T/dx^2 = 0.2 ; 0 ≤ x ≤ 10 T(0) = 40 & T(10) = 200. Use your experience in numerical differentiation and the finite difference technique with spacing, Δx = h = 2.0, obtain a corresponding set of algebraic equations. (The solution of the resultant system is not required, only write the matrix form).
Adi S.
Solve the Q
Jacob F.
Solve the boundary value problem. $$p^{\prime \prime}+2 p^{\prime}+2 p=0, \quad p(0)=0, \quad p(\pi / 2)=20$$
Differential Equations
Linear Second-Order Differential Equations
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD