If the equation of the curve which passes through the point $(1,1)$ satisfies the differential equation $\frac{d y}{d x}=\frac{2 x-5 y+3}{5 x+2 y-3}$, then the equation of that curve is

The general solution of the differential equation $\left(6 x^{2}-2 x y-18 x+3 y\right) d x-\left(x^{2}-3 x\right) d y=0$ is

If $y=\sin x+A \cos x$ is general solution of $\frac{d x}{d y}+f(x) y=\sec x$, then an integrating factor of the differential equation is

If $A$ and $B$ are arbitrary constants, then the differential equation having $y=A e^{-x}+B \cos x$ as its general solution is

The general solution of the differential equation $\frac{d y}{d x}+\frac{\sin (2 x+y)}{\cos x}+2=0$ is

The general solution of the differential equation $(9 x-3 y+5) d y=(3 x-y+1) d x$ is

The general solution of the differential equation $\frac{d y}{d x}=\frac{2 y^2+1}{2 y^3-4 x y+y}$ is

The general solution of the differential equation $\left(3 x^2-2 x y\right) d y+\left(y^2-2 x y\right) d x=0$ is

If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with origin as its focus and $X$-axis as its axis, then $m n-m+n=$

The general solution of $\frac{d y}{d x}+y f^{\prime}(x)-f(x) f^{\prime}(x)=0$, $y \neq f(x)$ is