
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 5th, 2017, 11:56 AM  #1 
Member Joined: May 2016 From: Ireland Posts: 96 Thanks: 1  equation
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. Last edited by skipjack; September 5th, 2017 at 12:43 PM. 
September 5th, 2017, 01:22 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,908 Thanks: 1382 
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? 

Tags 
equation 
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 09:40 PM 
Equation jump in graphical algebra equation  DarkX132  Algebra  3  September 26th, 2014 10:15 PM 
Gompertz equation  differential equation  Sonprelis  Calculus  6  August 6th, 2014 10:07 AM 
Show that an equation satisfies a differential equation  PhizKid  Differential Equations  0  February 24th, 2013 10:30 AM 
simplify equation to get a quadratic equation  mich89  Algebra  3  January 9th, 2013 01:22 PM 