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