Find the general solution of the given differential equation. x dy dx − y = x2 sin(x) y(x) = cx−xcos(x) correct: your answer is correct. 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.) incorrect: your answer is incorrect. 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.)

Note that in order to do this division, we cannot allow . This means the largest interval on which a solution can exist is either or .

If is a solution to the ODE, then any term that vanishes as (or , depending on which interval above is used) is a transient term.

Solve the ODE:

As , will oscillate between -1 and 1, so will oscillate between and , so the limit of as does not exists. There are no transient terms.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation: