 #1
cheapstrike
 42
 1
Homework Statement
Find the order of the differential equation of y=C_{1}sin^{2}x+C_{2}cos2x+C_{3}.
Homework Equations

The Attempt at a Solution
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I read in my book that the order of the differential equation is equal to the number of arbitrary constants but the answer given is 2.
Btw I have uploaded two pics with two methods I tried.
1st Pic  http://imgur.com/Py7DTgp
2nd Pic  http://imgur.com/5pdcWq1
In first picture, I calculated upto 3rd differential and obtained a differential equation.
In second picture, I differentiated both sides w.r.t. x and then sent the sin2x term, which I was getting in RHS, to LHS and wrote (1/sin2x) as cosec2x. Then I differentiated both sides again w.r.t. x. In this way, both C1 and C2 which remained after calculating 1st derivative become zero.
Which one is correct method? If it's neither, then what's the right method?