Question

Find the general solution, i.e. solution with precision up to some constant C , of the following differential equation:

dy/dx=2x

Answer 1

To find the general solution of the differential equation dy/dx = 2x, integrate both sides with respect to x. The general solution is y = x^2 + C.

Step-by-step explanation:

To find the general solution of the differential equation dy/dx = 2x, we can integrate both sides with respect to x. Integrating dy/dx gives us y, and integrating 2x gives us x^2. So the general solution is y = x^2 + C, where C is a constant.

If you want to verify this solution, you can differentiate y = x^2 + C with respect to x and see if you get 2x as the derivative. Additionally, you can substitute different values of x into the equation to see if it satisfies the original differential equation.