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missbossyy

Member

Registered: 2008-02-01

Posts: 38

Differentail Equations

Verify functions are solution of given differential equations.
1. dy/dx -2y = e^3x;  y=e^(3x) + 10 e^(2x)

2.       y' + y = sin x;  y= 1/2 sin x - 1/2 cosx + 10 e^(-x)

3.[(y')^3 + x y' =y; y=x+1

Last edited by missbossyy (2008-05-14 04:44:04)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Differentail Equations

Since you're asked to verify, you just need to make sure the given solution works (so you don't have to show how to find it).

So for 1) you'd differentiate y to get dy/dx = 3e^(3x) + 20e^(2x).
Then you have dy/dx = 3e^(3x) + 20e^(2x) -2[ e^(3x) + 10e^(2x)] = e^(3x), which is what you wanted. Incidentally, that 10 could be turned into an arbitrary constant if you felt like it.

2) and 3) are done in the same way.

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Why did the vector cross the road?
It wanted to be normal.

missbossyy

Member

Registered: 2008-02-01

Posts: 38

Re: Differentail Equations

yeay! i was on right track....
thank you so much....u r help and time is much appreciated :-)