Find a general solution to the differential equation given below. Primes denote derivatives with respect to $x$.
$$8y^{\prime \prime }+10y^{\prime }=0$$
The general solution of the differential equation is $y(x)=$

Step 1 ：We are given the homogeneous second order linear differential equation with constant coefficients: $8y^{\prime \prime }+10y^{\prime }=0$.

Step 2 ：The general form of such an equation is $a{y}^{″}+b{y}^{\prime }+cy=0$. The general solution to such an equation is given by $y(x)=C_1{e}^{m_{1}x}+C_2{e}^{m_{2}x}$, where $m_1$ and $m_2$ are the roots of the characteristic equation $a{m}^2+bm+c=0$ and $C_1$ and $C_2$ are arbitrary constants.

Step 3 ：In this case, $a=8$, $b=10$, and $c=0$. So the characteristic equation is $8m^2+10m=0$.

Step 4 ：The roots of the characteristic equation are $m_1=0$ and $m_2=-\frac{5}{4}$.

Step 5 ：Therefore, the general solution to the differential equation is $y(x)=C_1{e}^{0x}+C_2{e}^{-\frac{5}{4}x}=C_1+C_2{e}^{-\frac{5}{4}x}$.

Step 6 ：$\boxed{{\displaystyle \text{Final Answer: The general solution to the differential equation is }y(x)=C_1+C_2{e}^{-\frac{5}{4}x}}}$