Question

is y=cos(3x)+2x^2 a solution to y'' + (x/y) = 4cos(3x) + 4

Answer 1

What's the second derivative of the solution?

Answer 2

this is all the information i got :S

Answer 3

is there a way for me to solve this ?

Answer 4

You have everything you need, but you need to find the second derivative of \(y\) if you want to get anywhere.

Answer 5

do you mean y'' = 9cos(3x) + 4 ?

Answer 6

Close, the first term should be negative.

Answer 7

Now you substitute \(y\) and \(y''\) into the given equation:
\[(-9\cos3x+4)+\frac{x}{\cos3x+2x^2}\stackrel{?}=4\cos3x+4\]
If the equation is true, then \(y\) is indeed a solution.

Answer 8

i see, so my next move is to multiply through all the equation and then simplify :) ?

Answer 9

Yes. If you end up with \(\text{expression}=\text{expression}\), you're done.

Answer 10

okay okay, Thank you for all your help I really appreciate it :D

Answer 11

You're welcome