Exponentially sinusoidal

Consider the function

$f(y) = \displaystyle \int_{0} ^{\infty} [e^{(-x^2)} \sin(2xy)] \, dx$

Let $A$ , $B$ , $C$ and $D$ respectively be the coefficients of $\frac{d(f(y))}{dy}$ , $yf(y)$ , $y$ and $y^0$ in the first order differential equation of $f(y)$ .

$A\frac{d(f(y))}{dy}+ Byf(y)+Cy+D=0$ where it is also given that $A$ is positive .

further $f(y)$ can be expressed as follows

$f(y)= \int_{0} ^{y} [e^{(px^2)-(qy^2)}] \, dx$

Then evaluate $A+B+C+D+p+q$

Note that $A, B, C, D, p, q$ are real numbers and they have no common factor