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emworden90
 one year 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
emworden90
 one year 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
 one year 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
 one year 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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