Final answer:
To find the explicit general solution to the differential equation dy/dx + 20xy = 0, perform separation of variables, integrate both sides, and then find the exponential of the resulting expression to solve for y, yielding y = Ce^(-10x^2) as the solution.
Step-by-step explanation:
The differential equation dy/dx + 20xy = 0 is a first-order linear ordinary differential equation that can be solved using the method of separation of variables. The first step is to rearrange the terms to separate the variables x and y on opposite sides:
dy/y = -20x dx
Next, we integrate both sides:
∫ dy/y = ln|y| + C1
- ∫ -20x dx = -20x2/2 + C2
After integrating, we combine the constants of integration and exponentiate both sides to solve for y:
y = Ce-10x2
where C is the constant of integration which will be determined by the initial conditions of the problem. This function represents the explicit general solution to the given differential equation.