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Check the answer of a differential equation when I put it in Wolfram Alpha?

GROUPS:

This: y'''+4y'=sec2x

http://www.wolframalpha.com/input/?i=y%27%27%27%2b4y%27=sec2x

brings me this answer:

answer

So the circled with red it's incorrect in my opinion

answerwithred

Probably the first mistake causes the second.

What do you think?

POSTED BY: jorge aldape
Answer
4 months ago

Doing this in three steps to get it to fit within the line length limitation

If the supposed solution to the DE is

C1 Sin[2x]+C2 Cos[x]^2+C3-x Cos[2x]/4-Log[Cos[x]-Sin[x]]/8+Log[Sin[x]+Cos[x]]/8+Sin[2x]Log[Cos[2x]]/8

then the third derivative seems to be

third

which is also

-(Sec[2 x] (-2+8 C1+Log[Cos[2 x]]+Cos[4 x] (8 C1+Log[Cos[2 x]])+2 (-2 C2+x) Sin[4 x]))/2

and four times the first derivative seems to be

fourfirst

which is also

Cos[2 x] (8 C1+Log[Cos[2 x]])+2 (-2 C2+x) Sin[2 x]

and the sum of those seems to be

sum

which is also

Sec[2 x]

Can you explain exactly where in these steps you seem to see an error and what the error seems to be?

POSTED BY: Bill Simpson
Answer
4 months ago

enter image description here

POSTED BY: jorge aldape
Answer
4 months ago

Group Abstract Group Abstract