Final answer:
The solution to the differential equation dy/dx = 5xy is found by separating variables and integrating both sides, resulting in y = ±e^((5/2)x² + C) where C is the constant of integration.
Step-by-step explanation:
The solution to the differential equation dy/dx = 5xy, assuming that y ≠ 0, involves a process known as separation of variables. To solve for y, we integrate both sides; this gives us:
1/y dy = 5x dx
Integrating both sides:
ln(|y|) = (5/2)x² + C
Exponentiating both sides to eliminate the natural logarithm, we get:
y = ±e^((5/2)x² + C)
Here, C is the constant of integration, which can be determined given an initial condition for y.