![]() |
|
Differential Equations Ordinary and Partial Differential Equations Math Forum |
![]() |
| LinkBack | Thread Tools | Display Modes |
February 7th, 2018, 09:56 AM | #1 |
Newbie Joined: Feb 2018 From: Philippines Posts: 2 Thanks: 0 | ![]()
Can somebody help me with this differential equation? Thank you very much ![]() y''' + y'' + y = x^2 + 3e^3x |
![]() |
February 7th, 2018, 10:32 AM | #2 |
Senior Member Joined: Sep 2015 From: USA Posts: 2,320 Thanks: 1232 |
mathematica returns an absurdly long answer. are you sure there are no typos? |
![]() |
February 7th, 2018, 08:33 PM | #3 |
Banned Camp Joined: Apr 2017 From: durban Posts: 22 Thanks: 0 Math Focus: Algebra |
hmmm
|
![]() |
February 7th, 2018, 09:24 PM | #4 |
Math Team Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra |
The principal problem is that the characteristic (homogeneous) equation doesn't have pleasant roots.
|
![]() |
February 8th, 2018, 06:30 AM | #5 |
Newbie Joined: Feb 2018 From: Philippines Posts: 2 Thanks: 0 | |
![]() |
February 8th, 2018, 10:47 AM | #6 |
Global Moderator Joined: Dec 2006 Posts: 20,307 Thanks: 1976 |
If the equation is $y'' + y' + y = x^2 + 3e^{3x}$, a particular solution is $y = x^2 - 2x + \frac{3}{13}e^{3x}$. Add to that the general solution of $y'' + y' + y = 0$. |
![]() |
February 8th, 2018, 04:26 PM | #7 |
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 |
The characteristic equation for y''+ y'+ y= 0 is $r^2+ r+ 1= 0$. Writing that as $r^2+ r= -1$ and "completing the square", $r^2+ r+ \frac{1}{4}= (r+ \frac{1}{2})^2= -1+ \frac{1}{4}= -\frac{3}{4}$. Taking the square root of both sides $r+ \frac{1}{2}= \pm\frac{\sqrt{3}}{2}i$ and $r= -\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$. The general solution to that homogeneous differential equation is $y(x)= e^{-x/2}\left(C_1\cos(x\sqrt{3}/2)+ C_2\sin(x\sqrt{3}/2)\right)$ Last edited by skipjack; February 8th, 2018 at 05:56 PM. |
![]() |
![]() |
|
Tags |
differential, equation, problem |
Thread Tools | |
Display Modes | |
|
![]() | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Differential Equation Problem 2 | BonaviaFx | Calculus | 6 | July 19th, 2015 09:45 AM |
Differential equation problem | greg1313 | Differential Equations | 11 | July 12th, 2011 12:38 AM |
Help with differential equation problem | sivela | Differential Equations | 1 | January 21st, 2011 06:53 PM |
Differential equation problem! | David McLaurin | Differential Equations | 3 | July 8th, 2009 08:50 AM |
differential equation problem | Crumboo | Differential Equations | 0 | November 20th, 2007 04:35 AM |