My Math Forum Does anyone know how to solve this ODE question?

 Calculus Calculus Math Forum

 September 23rd, 2015, 09:21 AM #1 Member     Joined: Nov 2014 From: SG Posts: 55 Thanks: 1 Does anyone know how to solve this ODE question?
 September 23rd, 2015, 10:14 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 That looks like a fairly straightforward "second order, non-homogeneous, differential equation with constant coefficients". First find the general solution to the "associated homogeneous equation", $\displaystyle y''+ 4y= 0$. The "characteristic equation" is $\displaystyle r^2+ 4= 0$ which has roots $\displaystyle \pm 2i$. That means that the general solution to the homogeneous equation is $\displaystyle y(x)= C_1 \cos(2x)+ C_2 \sin(2x)$. Now we need to find a single solution to the entire equation. Normally, seeing "cos(2x)" on the right we would try "y(x)= A cos(2x)+ B sin(2x)" but that is already a solution to the homogeneous equation. So we try instead "y(x)= Ax cos(2x)+ Bx sin(2x)". With that y, what is y''? Putting that into the differential equation, what equation for A and B do you get? Last edited by skipjack; September 23rd, 2015 at 10:58 AM.
 September 23rd, 2015, 10:44 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,810 Thanks: 2151 Would you (KaiL) be able to finish if we suggest how you can start? For example, you could start by multiplying the equation by sin(2x), which gives an equation that can be integrated to give a first order ODE.

 Tags ode, question, solve

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post wasd3123 Linear Algebra 7 November 20th, 2013 10:11 AM mungbean_jones Economics 2 May 11th, 2011 10:24 PM bedii Real Analysis 2 October 3rd, 2009 01:47 PM alpah Number Theory 2 December 25th, 2006 09:51 PM mungbean_jones Abstract Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top