Verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval. 2x2y'' + 5xy' + y = x2 − x; y = c1x−1/2 + c2x−1 + 1 15 x2 − 1 6 x, (0, [infinity]) The functions x−1/2 and x−1 satisfy the differential equation and are linearly independent since W(x−1/2, x−1) = ≠ 0 for 0 < x < [infinity]. So the functions x−1/2 and x−1 form a fundamental set of solutions of the associated homogeneous equation, and yp = is a particular solution of the nonhomogeneous equation.

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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