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Theresa Archer 2022-06-27 Answered
I was solving differential equation
x cos x d y d x + y ( x sin x + cos x ) = 1
which on dividing by x cos x becomes FOLD(first order linear differential) equation.
But I am stuck at following integral. Can anyone help solve this integral? An alternate approach to the problem is also welcome.
e cos x cos x d x
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Answers (2)

hofyonlines5
Answered 2022-06-28 Author has 12 answers
By dividing both sides by cos 2 x we get
( x sec x ) d y d x + ( x tan x sec x + sec x ) y = sec 2 x d d x [ ( x sec x ) y ] = sec 2 x
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Arraryeldergox2
Answered 2022-06-29 Author has 10 answers
Step 1: multiply by dx
Step 2: ( x y sin x + y cos x 1 )   d x + x cos x   d y = 0
M = ( x y sin x + y cos x 1 )   and   N = x cos x
Step 3: Check if exact, i.e. if M y = N x (Hint, this is not exact)
Step 4: M y N x N = 2 tan x     i.e. is a function of x only
Now use integrating factor
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