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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 January 31st, 2012, 03:51 PM #1 Newbie   Joined: Jan 2012 Posts: 25 Thanks: 0 Ordinary differential equation y' = 2y + 4 Hey guys, I have to solve this by finding a constant solution and writing y(t) = y_h(t) + y_p(t). So far I have: y' = 2y + 4 y_p = at + b (at + b)' - 2(at + b) = 4 a - 2at - 2b = 4. Now I am stuck. Also, my notes say to set y' = 0, but I am not sure what that means exactly. Any help? January 31st, 2012, 05:23 PM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Ordinary differential equation y' = 2y + 4 We are given the ODE: If I were after the general solution, I would first arrange it as: then multiply through by the integrating factor : Integrate with respect to t: However, you are instructed to find the solution to the corresponding homogeneous equation and a particular solution: The associated auxiliary equation is: Thus: Using the method of undetermined coefficients, we assume a particular solution of the form: where A is an arbitrary real constant, and thus: Substituting into the ODE gives: Thus, by the principle of superposition, we have: January 31st, 2012, 11:57 PM   #3
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Re: Ordinary differential equation y' = 2y + 4

Quote:
 Originally Posted by Norm850 Hey guys, I have to solve this by finding a constant solution and writing y(t) = y_h(t) + y_p(t). So far I have: y' = 2y + 4 y_p = at + b (at + b)' - 2(at + b) = 4 a - 2at - 2b = 4. Now I am stuck. Also, my notes say to set y' = 0, but I am not sure what that means exactly. Any help?
a - 2at - 2b = 4. any value of t. So a = 0 and -2b=4
But this gives ony one solution of the ODE, not all.

dy/dx=2y+4 = 2(y+2)
dy/(y+2) ) =2 dx
ln(y+2)=2x+constant
y=C*exp(2x) -2 Tags differential, equation, ordinary Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post aheed Differential Equations 3 February 22nd, 2014 07:03 AM nehal Calculus 1 December 6th, 2013 12:27 PM nitin7785 Differential Equations 0 November 7th, 2013 12:22 AM WhatJac3 Algebra 10 April 20th, 2010 02:07 AM allison711 Differential Equations 3 February 8th, 2008 08:19 AM

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