statement – i : if y = 3e 2x + 2e 3x then d 2y dx 2 − 5 dy dx + 6y = 0 statement – ii : d dx (e mx) = me mx a. if both statement-i and statement-ii are true and statement-ii is the correct explanation of statement-i b. if both statement-i and statement-ii are true and statement-ii is not the correct explanation of statement-i c. if statement-i is true but statement-ii is false d. if statement-i is false but statement-ii is true
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Step-by-step explanation:
Given : y=3e
2x
+2e
3x
⟹
dx
dy
=3e
2x
×2+2e
3x
×3=6e
2x
+6e
3x
∴
dx
dy
=6e
2x
+6e
3x
dx
2
d
2
y
=6e
2x
×2+6e
3x
×3
=12e
2x
+18e
3x
Consider,
dx
2
d
2
y
−5
dx
dy
+6y
=12e
2x
+18e
3x
−5(6e
2x
+6e
3x
)+6(3e
2x
+2e
3x
)
=12e
2x
+18e
3x
−30e
2x
−30e
3x
+18e
2x
+12e
3x
=30e
2x
+30e
3x
−30e
2x
−30e
3x
=0
Hence,
dx
2
d
2
y
−5
dx
dy
+6y=0
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