Problem: When a certain drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after t hours is modeled by: D(t)= 50e-0.2t 1. What is the amount of the drug at the moment it is administered? 2. How many milligrams of the drug remain in the patient's bloodstream after 3 hours? 3. What will be the amount of drug left in the bloodstream as t goes to inifinity?

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Q: dy =x+3x + e2x dx 1. Solve the initial value problem when x-0. y-2.

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Q: Q4: Solve the initial value problem: ty = 2y + t

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Q: [3 Marks] B1(b): Solve the initial value problem: f'(x) = x10 + 12x + 15 and f(0) = 7.

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Q: Part II Solve the initial value problem. b. 3y(x?- 1) dx+ ( x³+ 8y– 3x) dy=0 y (0) = 1

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Q: 3. Solve the initial value problem hp? 4x² – x – 2 | y(1) = 1. dx (x + 1)(y+1)’

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.