# FP2 Second Order Differential Equation Q

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#1
The question:

http://i.imgur.com/8K7p32n.png

I let the PI = x2ex but when I substitute this into the differential equation I obtain a invalid solution

http://i.imgur.com/HXOXFgF.jpg

Why is this?
0
7 years ago
#2
Check the of partial integral.

Hope that helps.
0
#3
(Original post by lazy_fish)
Check your second derivative of partial integral.

Hope that helps.
Just corrected my mistake. However, I still get an invalid solution (albeit a different one); 2ex = ex ?

Thanks
0
7 years ago
#4
That is because your particular integral is not correct. It may be clear through inspection but a more systematic approach would be through:

Set a trial .

Do same thing, that is find and before using in original differential equation, and you'll end up solving for .

Substitute this value back into trial to get a particular integral.

Good luck.
0
#5
(Original post by lazy_fish)
That is because your particular integral is not correct. It may be clear through inspection but a more systematic approach would be through:

Set a trial .

Do same thing, that is find and before using in original differential equation, and you'll end up solving for .

Substitute this value back into trial to get a particular integral.

Good luck.
I was actually provided with the PI in a subtle manner (I didn't notice it earlier lol). The question says ''show that y = 0.5x2ex is a solution of the differential equation''. This may be quite obvious but how do I know that y = 0.5x2ex represents the particular integral?
0
7 years ago
#6
A particular integral is another term for particular solution so just plug it into and thus show it satisfies the original differential equation.
1
7 years ago
#7
(Original post by lazy_fish)
...
(Original post by GPODT)
...
Did you guys get this as your solution at the given boundary conditions?

0
7 years ago
#8
Yes.
0
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