Question
Convert the second order coupled system of ordinary differential equations$$\ddot{u}=a \dot{u}+b \dot{v}+c u+d v, \quad \ddot{v}=p \dot{u}+q \dot{v}+r u+s v,$$into a first order system involving four variables.
Step 1
Define: $$ w = \dot{u} \quad \text{and} \quad x = \dot{v}. $$ This implies that: $$ \dot{w} = \ddot{u} \quad \text{and} \quad \dot{x} = \ddot{v}. $$ Show more…
Show all steps
Your feedback will help us improve your experience
Christian Otero and 56 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
Convert the system of first-order differential equations into a single second-order differential equation: u' = 5u + 3v v' = 2u - v u'' - 11u = 0 u'' + 4u' = 0 u'' + 4u' + 11u = 0 u'' - 4u' + 11u = 0 u'' - 4u' - 11u = 0
Convert the given linear differential equations to a first-order linear system. $$y^{\prime \prime}+a y^{\prime}+b y=F(t), \quad a, b \text { constants. }$$
Systems of Differential Equations
First-Order Linear Systems
Convert the given system of differential equations to a first-order linear system. $$\frac{d x}{d t}-t y=\cos t, \quad \frac{d^{2} y}{d t^{2}}-\frac{d x}{d t}+x=e^{t}$$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD