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A Flipped Differential Equation 

SyberMath
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5 окт 2024

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Комментарии : 16   
@skwbusaidi
@skwbusaidi 5 месяцев назад
You can also solve by multiplying by 1-cosz We get Cosz(1-cosz)/sin^2 z = (cosz-cos^2 z)/ sin^2 z = cscz cotz - cot^2 z = cscz coz +1-csc^2 z Now integerate -cscz + z + cotz = x+c Final answer y + cot(x+y) - csc(x+y) = c
@ozgurtankut7404
@ozgurtankut7404 5 месяцев назад
Is it impossible that we just rewrite the question as "dy/dx=cos(y+x)", solve it for y and then name all x's as y and all y's as x? I mean, cant we just substitue y with x and x with y and at the end turn them again?
@ldanielmule8
@ldanielmule8 5 месяцев назад
I've got with that as well and though the inverse derivative theorem could simplify it a lot, but i'm not sure
@bkkboy-cm3eb
@bkkboy-cm3eb 5 месяцев назад
dx/dy=cos(x+y) x+y=u dx/dy+1=du/dy cos(u)+1=du/dy dy = du/(cos(u)+1) = (1-cos(u))/sin²(u)·du y = -1/tan(u) + 1/sin(u) + C y +1/tan(x+y) - 1/sin(x+y) = C
@NowInAus
@NowInAus 5 месяцев назад
Lovely and don’t apologise for going over 10 minutes!
@SyberMath
@SyberMath 5 месяцев назад
🥰
@Chrisoikmath_
@Chrisoikmath_ 5 месяцев назад
Can't we fine exactly y in terms of x and c only?
@subversively6680
@subversively6680 5 месяцев назад
PLZ, answer this Why flipping dx/dy Can not be solved as x is function of y?????
@kevinmadden1645
@kevinmadden1645 5 месяцев назад
I believe you are correct .
@Chrisoikmath_
@Chrisoikmath_ 5 месяцев назад
Sure! That's why the final equation is symmetric with respect to x and y.
@tixanthrope
@tixanthrope 5 месяцев назад
flipped does not mean much as the RHS is symmetrical in x and y.
@dominicellis1867
@dominicellis1867 5 месяцев назад
Does an explicit expression exist for this implicit solution?
@scottleung9587
@scottleung9587 5 месяцев назад
Nice!
@SyberMath
@SyberMath 5 месяцев назад
Thanks!
@84com83
@84com83 5 месяцев назад
Solving for "y", why not Forex?
@SyberMath
@SyberMath 5 месяцев назад
😜
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