Q. 104.7( 15 Votes )

# Form the differential equation representing the family of curves y = e^{2x}(a + bx) , where ‘a’ and ‘b’ are arbitrary constants.

Answer :

y=e^{2x}(a+bx)=ae^{2x}+bxe^{2x}

Differentiating with respect to x,

y’=2ae^{2x}+be^{2x}+2bxe^{2x}y’=2y+be^{2x} ..........(1)

Differentiating with respect to x,

y’’=2y’+2be^{2x}⇒ .........(2)

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

⇒ 2y’=4y+y’’-2y’

⇒ y’’-4y’+4y=0

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