Final answer:
To find the general solution of the given differential equation, separate the variables and solve for y. The largest interval over which the general solution is defined is (0, ∞).
Step-by-step explanation:
To find the general solution of the given differential equation, we can separate the variables and solve for y. The differential equation is dy/dx = 8y. Dividing both sides by y and dx, we get 1/y dy = 8 dx. Integrating both sides, we have ∫(1/y) dy = 8∫dx. This simplifies to ln|y| = 8x + C, where C is the constant of integration.
To find the largest interval over which the general solution is defined, we need to consider the domain of the natural logarithm function. Since ln|y| is defined only when y is positive, the interval of validity is when y > 0. Therefore, the largest interval over which the general solution is defined is (0, ∞).