Question
Solve $\ddot{x}-\dot{x}+x=0$ with $x_0=1$ and $v_0=0$ for $x(t)$ and sketch the response.
Step 1
The given equation is a second-order linear homogeneous differential equation: \[ \ddot{x} - \dot{x} + x = 0 \] Show more…
Show all steps
Your feedback will help us improve your experience
Anand Jangid and 65 other 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
Find $x=x(t)$ if $x(0)=0, \dot{x}(0)=1, \ddot{x}(0)=0$ and $\ddot{x}-\ddot{x}-\dot{x}+x=8 t e^{-t}$.
Differential Equations III: Higher-Order Equations
The Constant Coefficients Case
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD