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Question

Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.

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Solution

We have,y= Cx+5 .....1dydx=CSubstituting the value of C in 1, we gety= dydx×x+5xdydx-y+5=0 Hence, xdydx-y+5=0 is the differential equation representing the family of straight lines y=Cx+5, where C is an arbitary constant.

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