- #1

JulieK

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I have the following equation

[itex]\frac{\partial}{\partial y}\left(y\frac{dm}{dx}+m\frac{dy}{dx}\right)-\frac{dm}{dx}=0[/itex]

where [itex]m[/itex] is a function of [itex]y[/itex] (say [itex]m=f\left(y\right)[/itex]) and [itex]y[/itex] is a function of [itex]x[/itex] (say [itex]y=g\left(x\right)[/itex]). Are there any conditions under which [itex]\frac{dm}{dx}[/itex] becomes identically zero and hence this equation can be reduced to the follwoing form which is easier to solve:

[itex]\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0[/itex]

If such condtions do not exist, what is the best and easiest method to solve the original equation?

Note: I know [itex]f(y)[/itex] and I want to find [itex]g(x)[/itex] which is the function of interest to me.

I also wish to know if this equation can be solved numerically for g(x) if analytical solution is not possible.

[itex]\frac{\partial}{\partial y}\left(y\frac{dm}{dx}+m\frac{dy}{dx}\right)-\frac{dm}{dx}=0[/itex]

where [itex]m[/itex] is a function of [itex]y[/itex] (say [itex]m=f\left(y\right)[/itex]) and [itex]y[/itex] is a function of [itex]x[/itex] (say [itex]y=g\left(x\right)[/itex]). Are there any conditions under which [itex]\frac{dm}{dx}[/itex] becomes identically zero and hence this equation can be reduced to the follwoing form which is easier to solve:

[itex]\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0[/itex]

If such condtions do not exist, what is the best and easiest method to solve the original equation?

Note: I know [itex]f(y)[/itex] and I want to find [itex]g(x)[/itex] which is the function of interest to me.

I also wish to know if this equation can be solved numerically for g(x) if analytical solution is not possible.

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