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
September 5th, 2017, 12:56 PM   #1
Joined: May 2016
From: Ireland

Posts: 96
Thanks: 1


Solve (d^2)y/d(x^2) =y given that dy/dx =1 and y=1 when x=0.

I am not sure how to do this. What should the limits for v dv be?

Question 1 is the worked answer to the question. I am not sure where they get v=1, as it is not given in the question.
Attached Images
File Type: jpg IOE.jpg (21.8 KB, 10 views)

Last edited by skipjack; September 5th, 2017 at 01:43 PM.
markosheehan is offline  
September 5th, 2017, 02:22 PM   #2
Global Moderator
Joined: Dec 2006

Posts: 20,113
Thanks: 1909

The image is difficult to read. When x = 0, v = dy/dx = 1.

As $v = \dfrac{dy}{dx}$, $y = \dfrac{d^2y}{dx^2} = \dfrac{dv}{dx} = \dfrac{dv}{dy}\cdot\dfrac{dy}{dx} = v\dfrac{dv}{dy}$.
Integrating $y = v\dfrac{dv}{dy}$ with respect to $y$ gives ${\small\dfrac12}v^2 = {\small\dfrac12}y^2 + c$, where $c$ is a constant.

Note: it's asserted that $v = -y$ won't work, but that's incorrect.

Is that sufficient help?
skipjack is online now  

  My Math Forum > College Math Forum > Differential Equations


Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Cartesian equation of loci from given complex equation max233 Algebra 2 March 31st, 2017 10:40 PM
Equation jump in graphical algebra equation DarkX132 Algebra 3 September 26th, 2014 11:15 PM
Gompertz equation - differential equation Sonprelis Calculus 6 August 6th, 2014 11:07 AM
Show that an equation satisfies a differential equation PhizKid Differential Equations 0 February 24th, 2013 11:30 AM
simplify equation to get a quadratic equation mich89 Algebra 3 January 9th, 2013 02:22 PM

Copyright © 2019 My Math Forum. All rights reserved.