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

if y=4x then you will substitute 4x in for y in the second equation.

8x + 4x = 18 combine like terms

12x = 18 divide by 12 on both sides

x = 18/12 or 3/2

now replace x in the first equation with 3/2 to get

y = 4 3/2

y = 6

the answer is a

(3/2,6)

hope that .

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