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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
11 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
11 months ago

enter image description here

POSTED BY: jorge aldape
Answer
11 months ago

Group Abstract Group Abstract