User:EGM6321.f12.team7.Marjanovic/report2/2.9

=R*2.9=

Problem 9: Euler Integrating Factor
Based on lecture notes Pages 3 - 4

Given: Integrating factor as a function of y only
Suppose $$\displaystyle h_x(x,y) = 0, $$ thus $$\displaystyle h $$ is a function of y only; then the integrating factor becomes

Find: Integrating factor
Find $$\displaystyle h $$

Solution: h(y)

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This solution was prepared without referring to previous solutions. To find $$\displaystyle h(y)$$ we can start by integrating equation 9.1 to get: $$\displaystyle \int^y \frac{h_y}{h} = \int^y \frac{1}{M}(N_x - M_y) $$ $$\displaystyle log[h(y)] = \int^y m(s)ds + k $$ Finally, raising both sides to the exponent, you get: $$\displaystyle h(y) = exp[\int^y m(s)ds + k] $$ with the term in the exponent being known as the primitive.
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