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# True-or-False: Correct substitution for the solution of the differential equation of the type $\large\frac{dy}{dx}$$=f(x,y),where f(x,y) is a homogeneous function of zero degree is y=vx. Can you answer this question? ## 1 Answer 0 votes Toolbox: • A homogeneous linear differential equation of the form \large\frac{dy}{dx}$$=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