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Year 12s: what will be the first way you research your future options? >>

Differential equation

Find the general solution of the differential equation

\displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x)

.

This one's a bit harder than the baby one earlier.

(edited 7 years ago)

Original post by Ano123

Find the general solution of the differential equation

\displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x)

.

This ones a bit harder than the baby one earlier.

What have you tried?

Original post by Ano123

Find the general solution of the differential equation

\displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x)

.

This one's a bit harder than the baby one earlier.

I would not know where to start :tongue:

:tongue:

Study Forum Helper

Original post by IYGB

I would not know where to start :tongue:

:tongue:

http://www.wolframalpha.com/input/?i=x%5E3y%27%27%27%2Bx%5E2y%27%27-2xy%27%2B2y%3Dtan(ln(x))

OP

Original post by RDKGames

http://www.wolframalpha.com/input/?i=x%5E3y%27%27%27%2Bx%5E2y%27%27-2xy%27%2B2y%3Dtan(ln(x))

Don't just cheat and use wolframalpha. Try the question.

Study Forum Helper

Original post by Ano123

Don't just cheat and use wolframalpha. Try the question.

I would...

Spoiler

OP

Original post by Zacken

What have you tried?

Classic

x=e^t

transforms it to

\displaystyle y'''(t)-2y''(t)-y'(t)+2y(t)=\tan (t)

.

Original post by Ano123

Classic

x=e^t

transforms it to

\displaystyle y'''(t)-2y''(t)-y'(t)+2y(t)=\tan (t)

.

Can you take it from there?

Hint: ~~standard C.F and P.I works~~ variation of parameters work

(edited 7 years ago)

OP

Original post by Zacken

Can you take it from there?

Hint: standard C.F and P.I works

PI?

Original post by Ano123

PI?

Ah yeah, should have tried it myself. Go for variation of parameters instead.

OP

Original post by Zacken

Ah yeah, should have tried it myself. Go for variation of parameters instead.

Bingo.

username1162972

Wot bludy hel is this.
Do i ned this for uni.

Posted from TSR Mobile

Original post by physicsmaths

Wot bludy hel is this.
Do i ned this for uni.

Posted from TSR Mobile

this is why you need to relearn DE's with me

Original post by Ano123

Find the general solution of the differential equation

\displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x)

.

This one's a bit harder than the baby one earlier.

Try differentiating it once or twice and see if you can substitute a fraction of the result(s) for tan(ln(x)) and set up through that sort of simultaneous equation an equation with fewer derivatives.
(Note that the derivative of x^3 is 3x^2 (the one to the right go the term of x^3 in and the same is true for all the powers of x in there, and that the derivatives of y have the opposite pattern, meaning hopefully a technique like above will make some ground.)

(edited 7 years ago)

Original post by Ano123

Bingo.

I was looking the variation of parameters method on the net but I cannot find anything with 3 derivatives.
Are you making these up?

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