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anonymous
 3 years ago
Find the general solution:
\[(3+y+2y^2\sin^2 x)dx + (x+ 2xy y\sin 2x)dy=0\]
anonymous
 3 years ago
Find the general solution: \[(3+y+2y^2\sin^2 x)dx + (x+ 2xy y\sin 2x)dy=0\]

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\partial M}{\partial y} = 1 + 4y\sin^2 x\] \[\frac{\partial N}{\partial x} = 1 + 2y  2y\cos 2x\] so i guess tis isnt exact? or did i do something wrong?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it's 2sin^2x......it's exact

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0u kno 1cos2x = 2sinx*sinx

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0actually um wateva u call it it's root((1cos2x)/2) = sinx

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int (3+y+2y^2 \sin^2 x)dx\] \[3x + xy + y^2(x  \sin x \cos x)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then i take derivative of y

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[x + 2yx  2y\sin x\cos x + g'(y) = x+2xy  y\sin 2x\] \[g'(y) = 2y\sin x \cos x  y\sin 2x\] \[g(y) = 2\sin x \cos x  \sin 2x\] so the G.S. would be \[3x + xy + y^2(x  \sin x \cos x) + 2\sin x \cos x  \sin 2x + C\] correct?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0u kno there's a direct solution for exact equations

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i dont remember xactly but it's smthin llike integrate m(x,y) keeping y/x as a constant = integrate n(x,y) not containing terms of x/y + c

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh that..yeah...im more comfortable with this though

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0im more comfortable when the solution is one thread instead of inconsistent
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