Consider the initial value problem 2ty' = 6y, y(1) =-2.

a. Find the value of the constant C and the exponent r so that y = Ctr is the solution of this initial value problem. y = help (formulas)

b. Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution. help (inequalities)

c. What is the actual interval of existence for the solution (from part a)? help (inequalities)

step-by-step explanation:

the monthly balance will be $75,000

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step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is