Since g(t) is a sum I'll have 2 equations.

I'm kind of confused on which forms of Y to use.

Would and ?

Printable View

- October 17th 2013, 05:31 AMMadSoulzFind the general solution of the given differential equation

Since g(t) is a sum I'll have 2 equations.

I'm kind of confused on which forms of Y to use.

Would and ? - October 17th 2013, 05:39 AMProve ItRe: Find the general solution of the given differential equation
No, you don't need to do two equations.

Have you evaluated the homogeneous equation's solution yet? - October 17th 2013, 05:49 AMMadSoulzRe: Find the general solution of the given differential equation
Do you mean ?

If so,

I can't find though. - October 17th 2013, 06:14 AMHallsofIvyRe: Find the general solution of the given differential equation
For "linear differential equations with constant coefficients" if the "right hand side" functions are those that we expect as solutions to a homogeneous equation, , , , powers of t, and products of those, then you can expect such functions as solutions of the equation.

Here, the right side is 7sin(2t)+ 5t cos(2t). So try a solution of the form y= Asin(2t)+ Bcos(2t)+ Ctsin(2t)+ Dtcos(2t).

Then y'= 2A cos(2t)- 2B sin(2t)+ Ct cos(2t)+ C sin(2t)- Dt sin(2t)+ D cos(2t)= (Ct+ 2A+ D)cos(2t)+ (C-2B- Dt) sin(2t) and

y''= C cos(2t)- 2(Ct+ 2A+ D)sin(2t)- D sin(2t)+ 2(C- 2B- Dt) cos(2t).

Put those into the differential equations to get equations to solve for A, B, C, and D. - October 17th 2013, 07:18 AMMadSoulzRe: Find the general solution of the given differential equation
I was able to get that A=11/9, B=0, C=0, and D=-5/3.

But based off of my answer choices A should equal either 1/9 or -7/9. - October 17th 2013, 10:45 AMSlipEternalRe: Find the general solution of the given differential equation
HallsofIvy made a calculation error or two.

So and . Hence , , and .

That's closer to what you were expecting... - October 17th 2013, 11:51 AMMadSoulzRe: Find the general solution of the given differential equation
Thanks to you all.

So do I ever need to have 2 or more individual equations when g(t) is a sum of equations to find the particular solution? I have a picture to show what I mean. - October 17th 2013, 11:57 AMHallsofIvyRe: Find the general solution of the given differential equation
One of these days I really have to learn arithmetic!

- October 17th 2013, 11:58 AMSlipEternalRe: Find the general solution of the given differential equation
You can solve them all at once or one at a time, however you prefer.

- October 17th 2013, 12:08 PMMadSoulzRe: Find the general solution of the given differential equation
Ok, thanks again to you all