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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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True-or-False: Correct substitution for the solution of the differential equation of the type $\large\frac{dy}{dx}$$=f(x,y)$,where f(x,y) is a homogeneous function of zero degree is $y=vx.$

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  • A homogeneous linear differential equation of the form $\large\frac{dy}{dx}$$=f(x,y)$ can be solved by substituting $y=vx$ and $\large\frac{dy}{dx}$$=v+x \large\frac{dv}{dx}$
If $F(\lambda _x ,\lambda _y)=\lambda^0F(x,y),$ then it is a homogenous function of degree zero
If a first order degree differential equation is expressible of the form $\large\frac{dy}{dx}=\frac{f(x,y)}{g(x,y)}$
Where $f(x,y)$ and $g(x,y)$ are homogenous functions of the same degree, it is a homogenous differential equation.
Such type of equation can be reduced to variable seperable form by the substitution $y=vx$
Therefore Correct substitution for the solution of the differential equation of the type $\large\frac{dy}{dx}$$=f(x,y)$,where $f(x,y)$ is a homogeneous function of zero degree is $y=vx.$ is $True$
answered May 22, 2013 by meena.p
 

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