Find the solution of the given initial value problem. ty' + 2y = sin t, y π 2 = 9, t > 0 y(t) =

For the ODE

multiply both sides by t so that the left side can be condensed into the derivative of a product:

Integrate both sides with respect to t :

Divide both sides by to solve for y :

Now use the initial condition to solve for C :

So the particular solution to the IVP is

or

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.