Question

What is a solution to the differential equation `dy/dx=x^2y`?

Answer 1

`y=Ce^(x^3/3)`

Explanation:

First, separate the variables:

`dy/dx=x^2y" "=>" "dy/y=x^2dx`

Integrate both sides:

`intdy/y=intx^2dx" "=>" "ln(y)=x^3/3+C`

Solve for `y`:

`y=e^(x^3/3+C)=e^(x^3/3)(e^C)=Ce^(x^3/3)`