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 2 years ago
Determine whether or not the following equation is exact, find the solution. If not, use an integrating factor to convert it into exact and solve it. 2e^(x/2 +y)  y + 2((xe ^(x/2 +y) + 1) )dy/dx = 0 , y(0) = 1
 2 years ago
Determine whether or not the following equation is exact, find the solution. If not, use an integrating factor to convert it into exact and solve it. 2e^(x/2 +y)  y + 2((xe ^(x/2 +y) + 1) )dy/dx = 0 , y(0) = 1

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vf321
 2 years ago
Best ResponseYou've already chosen the best response.1A DE is exact iff, when in the form \[M dx + Ndy = 0\]that \(\frac{\partial M}{\partial x} = \frac{\partial N}{\partial x}\) because by Young's theorem this implies the existence of a relation \(\Psi(x, y) = C\) which can in turn be solved for \(y\).

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[2e^{x/2 +y}  y + 2(xe ^{x/2 +y} + 1) \frac{\mathrm dy}{\mathrm dx} = 0\] \[(2e^{x/2 +y}  y )\mathrm dx+ 2(xe ^{x/2 +y} + 1) \mathrm dy= 0\]
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