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Question

The family of curves passing through (0,0) and satisfying the differential equation y′′y=1 (where y=dydx and  y′′=d2ydx2) is 


Your Answer
A
y=k 
Your Answer
B
y=kx
Your Answer
C
y=k(ex+1)
Correct Answer
D
y=k(ex1)

Solution

The correct option is B y=k(ex1)
dpdx=p(where p=dydx)
lnp=x+cp=ex+c
dydx=kexy=kex+λ
Satisfying (0,0), So λ=k
y=k(ex1)
 

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