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![(4 marks) Solve the initial value problem, u'(t) = 2tu(t) + 6t with u(0) = 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5141e434-b582-4d21-ac72-758865899632%2Fa28ac2de-a94e-41cf-ae67-c9a79809daca%2Foq5f55b_processed.png&w=3840&q=75)
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- Based on data from 1997-2005, the amount of yogurt produced in the UnitedStates annually may be modeled byy(t) = 14.99t2 + 62.14t + 1555 million poundswhere t is the number of years since 1997.(a) Find and interpret the meaning of y(12).(b) Find and interpret the meaning of y'(12).23. (1.4) Solve y +2 = (4x + 2y + 6)-'e2r+v+3.2. Solve X': 0 (-23) x + (9)