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Question

(A) For a homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$,the variables are expressed as a function of the r

Vedclass · Accepted Answer

$x = vy$

Vedclass · Answer

(A) For a homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$,the variables are expressed as a function of the ratio $\frac{x}{y}$.To solve this,we substitute $x = vy$,where $v$ is a function of $y$.By differentiating $x = vy$ with respect to $y$,we get $\frac{dx}{dy} = v + y\frac{dv}{dy}$.Substituting this into the original equation allows us to separate the variables $v$ and $y$.Therefore,the correct substitution is $x = vy$.Hence,the correct option is $A$.

$A$ homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$ can be solved by making the substitution:

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