Form the differential equation representing the family of curves  ax+by=0, where a and b are arbitrary constants.

 

 

 

 
 
 
 
 

Answers (1)

Given equation is ax+by=0

Differentiating wrt x, we get

a+b\frac{\mathrm{d} y}{\mathrm{d} x}=0

b\frac{\mathrm{d} y}{\mathrm{d} x}=-a

\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{-a}{b}\: \: \: \: \rightarrow (1)

Again, differentiating (1) wrt x,

\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}=0

\therefore The differential equation is  y''=0.

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