Find a formula for y(t) with y(0)=1 and draw its graph. what is y\infty?
a. y'+2y=6
b. y'+2y=-6

Step-by-step explanation:

(a) Given differential equation is

   Y'+2Y=6

=>(D+2)y = 6

To find the complementary function, we will write

D+2=0

=> D = -2

So, the complementary function can be given by

To find the particular integral, we will write

         

           

           = 3

so, the total solution can be given by

         

but according to question

1 = C +3

=> C = -2

So, the complete solution can be given by

(b) Given differential equation is

   Y'+2Y=-6

=>(D+2)y = -6

To find the complementary function, we will write

D+2=0

=> D = -2

So, the complementary function can be given by

To find the particular integral, we will write

           

           

           = -3

so, the total solution can be given by

         

but according to question

1 = C -3

=> C = 4

So, the complete solution can be given by

Just a second zzz

The answer would he -4,-2 because the points are just on the opposite side. since the x axis is +4 it's going to he -4 and since the y axis is -2 it stays there because whaen rotated it stays in the third quadrant