How to you find the general solution of dy/dx=xcosx^2?

ymochelows 2022-09-14 Answered
How to you find the general solution of d y d x = x cos x 2 ?
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Answers (2)

Maggie Tanner
Answered 2022-09-15 Author has 18 answers
First we notice that
d sin x 2 d x = 2 x cos x 2
or
x cos x 2 = 1 2 ( d sin x 2 d x )
Hence the problem becomes
d y d x = 1 2 d sin x 2 d x
Integrate both sides with respect to x and we have
d y d x d x = 1 2 ( d sin x 2 d x ) d x
y = 1 2 sin x 2 + c
The general solution is
y ( x ) = 1 2 sin x 2 + c

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iescabroussexg
Answered 2022-09-16 Author has 4 answers
Another way
d y d x = x cos x 2
d y = x cos x 2 d x
d y = x cos x 2 d x
THIS SOLUTION IS ONLY CORRECT IF THE PROBLEM IS WRITTEN CORRECTLY. The solution would be different if the problem is d y d x = x cos 2 x .
Let u = x 2 . Then du=2xdx and d x = d u 2 x
d y = x cos u d u 2 x
d y = 1 2 cos u d u
y = 1 2 sin u + C
y = 1 2 sin ( x 2 ) + C

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