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

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lgbasallote Group TitleBest 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?
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
wait wat's 1cos2x?
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
it's 2sin^2x......it's exact
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
wait what?
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
u kno 1cos2x = 2sinx*sinx
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
oh i see your point
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
actually um wateva u call it it's root((1cos2x)/2) = sinx
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
so it's exact..
 2 years ago

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

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
then i take derivative of y
 2 years ago

lgbasallote Group TitleBest 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?
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
u kno there's a direct solution for exact equations
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
really? what?
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
i 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
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
oh that..yeah...im more comfortable with this though
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
im more comfortable when the solution is one thread instead of inconsistent
 2 years ago

A.Avinash_Goutham Group TitleBest ResponseYou've already chosen the best response.1
ok
 2 years ago
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