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

True-or-False: Correct substitution for the solution of the differential equation of the type $\large\frac{dx}{dy}$$=g(x,y)$,where $g(x,y)$ is a homogeneous function of zero degree is $x=vy.$

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  • A homogeneous linear differential equation of the form $\large\frac{dy}{dx}$$=f(x,y)$ can be solved by substituting $x=vy$ and $\large\frac{dx}{dy}$$=v+y \large\frac{dv}{dx}$
If the differential equation is a homogenous differential equation and expressible as a function of $\large\frac{x}{y}$.
Then we put $x=vy$ and $\large\frac{dx}{dy}$$=v+y \large\frac{dv}{dy}$
Correct substitution for the solution of the differential equation of the type $\large\frac{dx}{dy}$$=g(x,y)$,where $g(x,y)$ is a homogeneous function of zero degree is $x=vy.$ $True$
answered May 22, 2013 by meena.p
 

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