Question

what is the solution to this differential equation (with the given initial condition)? 4 hint: this is asking for a function that has a derivative of . what function do you have to start with to get that derivative? try using your knowledge of derivatives to guess the solution) c. what is the magnitude of the error in the two euler approximations you found? magnitude of error in euler with 2 steps

Answer 1

The solution to the differential equation is f(x) = 4x + C. The magnitude of the error in the Euler approximations can be found by calculating the absolute difference between the exact solution and the approximations.

Step-by-step explanation:

To find the solution to the given differential equation, we need to start with a function that has a derivative of 4. Let's call this function f(x). So, the derivative of f(x) will be 4. One such function is f(x) = 4x + C, where C is a constant. This function satisfies the condition that its derivative is 4, so it is the solution to the differential equation.

The magnitude of the error in the two Euler approximations can be found by calculating the absolute difference between the exact solution and the approximations at the same point. Let's say the exact solution is denoted by y(x) and the Euler approximations are denoted by y_1(x) and y_2(x) (with 2 steps), then the magnitude of the error in the Euler approximations is |y(x) - y_1(x)| and |y(x) - y_2(x)| respectively.