Solve the initial-value problem. x' + 2tx = 5t, x(0) = 8 x(t) =

Multiply both sides of the ODE

by :

Now the left side can be condensed as the derivative of a product:

Integrate both sides, then solve for x :

Given that x(0) = 8, we find

so that the particular solution to this IVP is

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98