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Uae c cxg t. ^ C D ȃg N ̃^ C X g ̏Љ A ̐ ̃T C g Yahoo!. C C′ This looks reasonable purely formally, since we get the right side by substituting into the left side the expressions for z and dz in terms of x and y z = f(x, y), dz = fxdx fydy To justify it more carefully, we use the parametrizations given above for C and C′ to calculate the line integrals t1 dz P (x, y, z)dz = P (x(t),y(t),z(t. N u c Y @ c A C x g u z K ΐV ԉΑ ƐM B ӍՁI v y z @ @ @ @ 쌧 z K S x m x m Ԓn.

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Y(t) = C e 2t, for any constant C That is, any function of this form, regardless of the value of C, will satisfy the equation y′ − 2 y = 0 While there are infinitely many such functions, no other type of functions could satisfy the equation The similar technique could also be used to solve this next example. G X e T @ A l J v A B S \ 񐧁@ v C x g T i P T l j B n C A G X e ̍ō ̖ Ȃ ɁB TwoRings Ёi E y j @ 1000 `20 j Y G X e ͂. O _ C i R A c SD K _ ^ T C g u v k @ r c f t m c ` l v.

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