What is the general potential function responsible for each of the following equations:
N naviakam New member Joined Dec 28, 2020 Messages 20 Jan 4, 2021 #1 What is the general potential function responsible for each of the following equations: Last edited: Jan 4, 2021
D Deleted member 4993 Guest Jan 4, 2021 #2 naviakam said: What is the general potential function responsible for each of the following equations: View attachment 24147 View attachment 24148 Click to expand... Please show us what you have tried and exactly where you are stuck. Please follow the rules of posting in this forum, as enunciated at: READ BEFORE POSTING Please share your work/thoughts about this problem.
naviakam said: What is the general potential function responsible for each of the following equations: View attachment 24147 View attachment 24148 Click to expand... Please show us what you have tried and exactly where you are stuck. Please follow the rules of posting in this forum, as enunciated at: READ BEFORE POSTING Please share your work/thoughts about this problem.
H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 7,763 Jan 5, 2021 #3 \(\displaystyle y'+ \frac{ny}{x}= 0\) \(\displaystyle \frac{dy}{dx}= -\frac{ny}{x}\) \(\displaystyle \frac{dy}{y}= -\frac{ndx}{x}\) Integrate. \(\displaystyle y''+ \frac{y'}{t}= 0\) Let u= y'. Then u'= y'' and the equation becomes \(\displaystyle u'+ \frac{u}{t}= 0\) \(\displaystyle \frac{du}{dt}= -\frac{u}{t}\) \(\displaystyle \frac{du}{u}= -\frac{dt}{t}\) Integrate. Since y'= u, dy= udt Integrate again.
\(\displaystyle y'+ \frac{ny}{x}= 0\) \(\displaystyle \frac{dy}{dx}= -\frac{ny}{x}\) \(\displaystyle \frac{dy}{y}= -\frac{ndx}{x}\) Integrate. \(\displaystyle y''+ \frac{y'}{t}= 0\) Let u= y'. Then u'= y'' and the equation becomes \(\displaystyle u'+ \frac{u}{t}= 0\) \(\displaystyle \frac{du}{dt}= -\frac{u}{t}\) \(\displaystyle \frac{du}{u}= -\frac{dt}{t}\) Integrate. Since y'= u, dy= udt Integrate again.
