Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation (7 minus t )y double prime plus 5 t y prime minus 7 y equals sine t, given that y (0 )equals 7 and y prime (0 )equals 7. If a conclusion can be drawn, discuss it. If a conclusion cannot be drawn, explain why.

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step-by-step explanation:

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i believe both

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james might might idk and tbh dont rly care

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81