Given the first order IVP y′+6y={5x4e−6x,0,0≤x<1x≥1 with initial condition y(0)=2. (1) Find the explicit solution on the interval 0≤x<1 y(x)= e^(-6x)(x^5+2) . (2) Find the limx→1y(x)= 3e^-6 . (3) Then find the explicit solution on the interval x≥1 y(x)= 1+(3-e^6)e^(-6x) .

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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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