Find a homogeneous linear DE with the following three solutions: e^x, xe^x, x^2e^x.
Added by Ramon H.
Close
Step 1
We want to find a homogeneous linear differential equation that has these solutions. Let's consider the Wronskian of these three functions. The Wronskian is given by the determinant of the following matrix: $$ W = \begin{vmatrix} e^x & xe^x & x^2e^x \\ e^x & Show more…
Show all steps
Your feedback will help us improve your experience
Benjamin Densmore and 81 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Linear independent solutions of the homogeneous part of the differential equation y '' - 2y '+ y = xe ^ x are y1 = e ^ x and y2 = xe ^ x. What is the special solution of the equation?
Sri K.
Solve the given non homogeneous system. $$x_{1}^{\prime}=x_{1}+x_{2}+e^{2 t}, \quad x_{2}^{\prime}=3 x_{1}-x_{2}+5 e^{2 t}$$
Systems of Differential Equations
First-Order Linear Systems
Find a linear homogeneous constant-coefficient equation with the given general solution. (A + Bx)e^(2x)
Avinash V.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD