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Differential Equations

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Nonlinear 1st order ODE: Homogeneous Equations

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Consider the equation:

$$y'=\frac{4y-3x}{2x-y}$$

Which of the following statements are TRUE?

A

This equation is separable.

B

This equation is equivalent to $(4y-3x)-(2x-y)y'=0$ which has an integrating factor of the form $\mu=\mu(x)$.

C

Let $v(x)=y(x)/x$. $v$ satisfies the equation $x(2-v)v'=v^2+2v-3$, which is separable.

D

This equation can't be solved in a closed form $F(x,y,C)=0$ such that $F$ is a function composed from power, rational, trigonometric, exponential and logarithmic functions, and $C$ is an arbitrary constant.