Equation is x"-4x=0, general solution is x(t) = c1e^-2t+c2e^2t, initial condition is x(0) = 1, x'(0)=0

Step-by-step explanation:

The given differential equation is

The characteristics equation is given by

Therefore, the solution of the DE is given by

On differentiating, we get

Apply the initial conditions

x(0)=1

Second condition is x'(0)=0

Add (i) and (ii)

Substituting this value in (ii)

Hence, the solution of the DE is

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step-by-step explanation:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt