Browse Questions

# 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

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

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 $C$