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
Let's choose a specific point/vertex on both parallelogram and see the changes;
Observing that A is (-4, 1) and A' is (4, -1).
From this we can observe that the graph was flipped over the x-axis because the x value went from negative to positive. Again, we see that the shape was flipped over the y-axis since the y values went from positive to negative.
From this scenario, the correct solution should be A.
Double check this by picking another vertex and comparing.
D's coordinates are (-2, 1) and D' is (2, -1)
Again, the x and the y values are flipped, meaning that this graph was flipped over the x-axis and y-axis, confirming our answer.
Hope I helped :)
