Q10 of 52 Page 1

Form the differential equation representing the family of curves y = e2x(a + bx) , where ‘a’ and ‘b’ are arbitrary constants.

y=e2x(a+bx)=ae2x+bxe2x


Differentiating with respect to x,


y’=2ae2x+be2x+2bxe2x

y’=2y+be2x ..........(1)


Differentiating with respect to x,


y’’=2y’+2be2x

⇒ .........(2)


Substituting (2) in (1), we get,



⇒ 2y’=4y+y’’-2y’


⇒ y’’-4y’+4y=0

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