Question

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y(x) is the solution of the differential equation
d y/d x=6 x y .
When x=0, y=1

Answer 1

The solution to the differential equation dy/dx = 6xy with the initial condition y(0)=1 is y = e^(3x^2).

Step-by-step explanation:

The question refers to solving a differential equation of the form d y/d x = 6 x y, with an initial condition when x=0, y=1. To find the solution y(x), we can separate the variables and integrate both sides. By separating, we get dy/y = 6xdx. Integrating both sides gives us ln(y) = 3x^2 + C, where C is the constant of integration. Using the initial condition, we find that C = 0, as ln(1) = 0. Thus, the solution is y = e^(3x^2).