Find the general solution of the given differential equation. x2y' + x(x + 2)y = ex y(x) = give the largest interval over which the general solution is defined. (think about the implications of any singular points. enter your answer using interval notation.) determine whether there are any transient terms in the general solution. (enter the transient terms as a comma-separated list; if there are none, enter none.)

Multiply both sides of the ODE by :

and notice that . So we can collapse the left side and write it as the derivative of a product:

We can't have , so (or , depending on the initial value) would be the largest interval over which the solution is valid.

As , we see the term rapidly approaching 0, so this is the only transient term.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet