If the solution of the differential equation $(2x+3y-2)dx+(4x+6y-7)dy=0$ with $y(0)=3$ is $\alpha x+\beta y+3 \log_e|2x+3y-\gamma|=6$,then $\alpha+2\beta+3\gamma$ is equal to

$A$ differentiable function satisfies $3f^2(x) f'(x) = 2x$. Given $f(2) = 1$,then the value of $f(3)$ is:

The solution of the differential equation $\frac{dy}{dx} - \frac{y+3x}{\log_{e}(y+3x)} + 3 = 0$ is (where $C$ is a constant of integration.)

The solution of the differential equation $3e^x \tan y \, dx + (1 - e^x) \sec^2 y \, dy = 0$ is

If $y=y(x)$ is the solution of the differential equation $\left(\frac{5+e^x}{2+y}\right) \frac{dy}{dx}+e^x=0$ satisfying $y(0)=1$,then a value of $y(\log 13)$ is

Let $f: R \rightarrow R$ be a differentiable function with $f(0)=0$. If $y=f(x)$ satisfies the differential equation $\frac{dy}{dx}=(2+5y)(5y-2)$,then the value of $\lim_{x \rightarrow -\infty} f(x)$ is: