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CBSE Class 12 Math 2018 Solved Paper

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Question : 10
Total: 29
Find the differential equation representing the family of curves y = aebx+5 , where a and b are arbitrary constants.
Solution:  
Given y = aebx+5
Differentiating with y with respect to x,
⇒
dy
dx
 = aebx+5 × b
⇒
dy
dx
 = by ... (i) (Since y = aebx+5)
Diffrentiating (i) with respect to x,
⇒
d2y
dx2
 = b
dy
dx
⇒
d2y
dx2
 = (
1
y
dy
dx
)
dy
dx
 ... from (i)
⇒ y
d2y
dx2
 = (
dy
dx
)2
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