My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum

LinkBack Thread Tools Display Modes
March 4th, 2019, 01:14 AM   #1
Joined: Mar 2019
From: Holland

Posts: 1
Thanks: 0

Question Help with differential equation

Hi, I'm new to this forum. Found this forum searching for help with a Math question. I need some help with a differential equation that I can't solve. I hope you guys can help me.

The equation
$\displaystyle \frac{d^2F}{dX^2}=-\frac{2\ast\sigma_s}{E\ast\left[\sqrt{4.65152d^2-26.853\frac{M}{\sigma_sd}-0.41955d}\right]}$

With the following replacements

$\displaystyle M=\frac{P}{2}\ast x$

$\displaystyle a=4.65152d^2$

$\displaystyle b=\frac{26.853}{2}\frac{P}{\sigma_s\ast d}$

$\displaystyle c=2\frac{\sigma_s}{E}$

$\displaystyle e=0.41955d$

We can rewrite the equation as: $\displaystyle \frac{d^2F}{dx^2}=\frac{c}{e-\sqrt{a-bX}}$

Boundary conditions: $\displaystyle x=\frac{L}{2}$, $\displaystyle \frac{dF}{dX}=0$

Solving this:

$\displaystyle dF/dx=\frac{2c\ast\left(e\ast\ln{\left(\sqrt{a-bx}\ast e\right)}+\sqrt{a-bx}\right)}{b}+C_1$

$\displaystyle C_1=-\frac{2c\ast\left(e\ast\ln{\left(\sqrt{a-b\frac{L}{2}\ }\ast e\right)}+\sqrt{a-b\frac{L}{2}}\right)}{b}$

Next we say the boundary conditions are:

$\displaystyle x=x_0$

$\displaystyle F=F_0=\frac{P}{d^4\ast E}\ast(\frac{4}{\pi}L^2\ast\ x_0-\frac{16}{3\pi}\ast\ x_0^3)$

with $\displaystyle x_0=\pi/16\ast\sigma_s/P\ast d^3$

This is the point where I don't know how to solve it anymore. I know what the solution is, but I want to know how they got there.

$\displaystyle F=2\frac{c}{b}\left\{-\frac{2}{3}\frac{\left(a-bX\right)^\frac{3}{2}}{b}-\frac{e}{b}\left[ln\left(\sqrt{a-bX}-e\right)\left(a-bX-e^2\right)+\frac{3}{2}e^2-e\sqrt{a-bX}-\frac{a-bX}{2}\right]\ \right\}+C_1X+C_2$

$\displaystyle C_1=-\frac{2c}{b}\left[\sqrt{a-b\frac{L}{2}}+e*ln\left(\sqrt{a-b\frac{L}{2}}-e\right)\right]$

$\displaystyle C_2=Y_0-\frac{2c}{b}\left\{-\frac{2}{3}\frac{\left(a-bX\right)^\frac{3}{2}}{b}-\frac{e}{b}\left[\ln{\left(\sqrt{a-bX_0}-e\right)\left(a-bX_0-e^2\right)+\frac{3}{2}e^2-e\sqrt{a-bX_0}-\frac{a-bX_0}{2}}\right]\right\}-K_1X_0$

Many thanks in advance.
Attached Images
File Type: jpg equation.JPG (94.4 KB, 1 views)

Last edited by skipjack; March 4th, 2019 at 04:43 AM.
snadur is offline  

  My Math Forum > College Math Forum > Differential Equations

differential, equation

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Differential equation max233 Calculus 4 March 26th, 2016 04:21 AM
Gompertz equation - differential equation Sonprelis Calculus 6 August 6th, 2014 11:07 AM
Differential equation consigliere Differential Equations 5 August 23rd, 2013 11:54 AM
Show that an equation satisfies a differential equation PhizKid Differential Equations 0 February 24th, 2013 11:30 AM
What's a differential equation? JohnC Differential Equations 4 March 9th, 2012 12:02 AM

Copyright © 2019 My Math Forum. All rights reserved.