Use the method of undetermined coefficients to solve the following differential equation: y′′+4y=4x

Step-by-step explanation:

given,

y′′ + 4 y = 4 x

D² y + 4 y = 4 x

(D²+4) y = 4 x

now, writing Auxiliary  equation

m² + 4 = 0

m² = -4

m = ± 2 i

now, complimentary function

a = 0 ,  b = 2

particular integral (y_p)

y_p = a x

y'_p = a

y"_p = 0

now,

y′′+ 4 y = 4 x

0+ 4 (a x )= 4 x

4 a x = 4 x

     a = 1

now,

  y_p = x

now, general equation

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation: