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Home  >>  CBSE XII  >>  Math  >>  Differential Equations

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

\[(A)\;y=\;vx\qquad(B)\;v=\;yx\qquad(C)\;x=\;vy\qquad(D)\;x=\;v\]

1 Answer

Toolbox:
  • A homogenous differential equation with $\large\frac{dx}{dy}$ can be solved by substituting $x = vy$ and $\large\frac{dx}{dy}$$ = v + x\large\frac{dv}{dy}$
Since the equation is of the form $\large\frac{dx}{dy} = $$h\big(\large\frac{x}{y}\big)$,using the information in the tool box we can solve the equation by substituting $x = vy.$
Hence the correct answer is $C$
answered Aug 1, 2013 by sreemathi.v
 

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