Answer:
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Step-by-step explanation:
Answer:
r = 1
Step-by-step explanation:
In this question, we have to solve for the vallue of "r". We will use the distributive property shown below to ease our process.
Distributive Property:
a(b+c) = ab + ac
Now, lets solve this:

As we have seen the value of r is "1"
Answer:

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

