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The differential equaiotn which represen...

The differential equaiotn which represents the family of curves `y=C_(1)e^(C_(2)x)`, where `C_(1)` and `C_(2)` are arbitrary constants, is

A

`y^(')=y^(2)`

B

`y^('')=y^(')y`

C

`yy^('')=y^(')`

D

`yy^('')=(y^('))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`y=c_(1)e^(c_(2)x)`………..(i)
`therefore y^(')=c_(2)c_(1)e^(c_(2)x)=c_(2)y`…………..(ii)
`therefore y^('')=c_(2)y^(')`………..(iii)
From (ii), we get
`c(2)=y^(')/y`
From (ii) and (iii)
We get `y^('')/y^(')=y^(')/y` or `yy^('')=y^('^(2))`
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