If $\int_{-a}^a f(x) d x=\int_0^a f(x) d x+\int_0^a g(x) d x$, then $g(x)=$

$f\left(x, y, c_1, c_2\right)=0$ is an equation containing two arbitrary constants $c_1$ and $c_2$. If the differential equation having $f\left(x, y, c_1, c_2\right)=0$ as its general solution is of $k$ th order, then the differential equation corresponding to $x^k+y^k=c^2$ ( $c$ is an arbitrary constant) is

If $l$ and $m$ are respectively the order and the degree of the differential equation $f(x) y^{\prime \prime}+g(x) y^{\prime}=\frac{4 y}{x}$ whose general solution is $y=a x^2+b x^2 \log x$, then $f(m)+g(m)=$

The general solution of the differential equation $d x=(2 x+3 y-4) d y$ is