Q.

Find the differential equation representing the family of curves y=aebx+5, where a and b are arbitrary constants.

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answer is 1.

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Detailed Solution

Given: curve y=aebx+5.....(1)
Differentiate that w.r.t. x, it follows
dydx=aebx+5ddx(bx+5) dydx=aebx+5b           ....(ii) dydx=yb             [From (i)]
Differentiating again w.r.t. x, we get
d2ydx2=dydxb d2ydx2=dydxdydx1y b=1ydydx yd2ydx2=dydx2
Therefore, the differential equation is yd2ydx2=dydx2.

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