NEED A HELP WITH THE FOLLOWING QUESTION

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YOU NEED TO ANSWER ALL QUESTIONS

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SO AS YOU KNOW THEN ANSWER ALL OF IT

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Find the general solution of the differential equation. (Enter your solution as an equation.) 1234 dx 2}! S Find the particular solution of the differential equation that satisfies the initial condition. [Enter your solution as an equation.) Differential Equation Initial Condition yy'2ex=0 y(0)=3 Find an equation of the curve that passes through the point and has the given slope. (Enter your solution as an equation.) 04 "=L L). y (W Find all functions f having the indicated property. (Enter your solution as an equation.) The tangent to the graph of fat the point (x, y) intersects the x-axis at (x + 99, 0). Find the general solution of the first-order linear differential equation for x > 0. (Use C for any needed constant.) y'+ 51/: e" Find the particular solution of the firstorder linear differential equation for X > O that satisfies the initial condition. Differential Equation Initial Condition y'+y=ex V(0)=3 Find the particular solution of the first-order linear differential equation for X > 0 that satisfies the initial condition. Differential Equation Initial Condition y'+y=6eX Y(0)=3 The management at a certain factory has found that the maximum number of units a worker can produce in a day is 60. The rate of increase in the number of units N produced with respect to time t in days by a new employee is proportional to 60 a N. (a) Determine the differential equation describing the rate of change of performance with respect to time. (Use k for the constant of proportionality.) dN : dt (b) Solve the differential equation from part (a). (Use Cfor any needed constant.) N: (c) Find the particular solution for a new employee who produced 15 units on the rst day at the factory and 25 units on the fteenth day. N