y = ae^x+be^-xprove that y2=y
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Answer:
⇒0
Step-by-step explanation:
We have,
y=ae
−2x
+be
x
On differentiating and we get,
dx
dy
=−2ae
−2x
+be
x
Again differentiating and we get,
dx
2
d
2
y
=4ae
−2x
+be
x
Now,
L.H.S.
dx
2
d
2
y
+
dx
dy
−2y
⇒4ae
−2x
+be
x
−2ae
−2x
+be
x
−2(ae
−2x
+be
x
)
⇒4ae
−2x
+be
x
−2ae
−2x
+be
x
−2ae
−2x
−2be
x
⇒4ae
−2x
−4ae
−2x
+2be
x
−2be
x
⇒0
Hence, this is the answer.
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