Week 9 - 1st Order Differential Equations

Question 1

a) Solve the differential equation y’(x) = y(x).

b) If we now specify that the initial condition is that  y(0) = 1 solve y’(x) = y(x).

c) Define a function as the answer to your differential equation.

d) Use the function you have defined above to plot the solution for the range of x from 0 to 5.

Question 2

A student is struggling to solve a problem in Mathematica to solve the differential equation y’(x) = -(6x+2)*y(x).  They show you that they have sets up the code as below. Evaluate the code to see the error the student would like to discuss.

DSolve[{y'[x]=-(6x+2)*y[x]},y[x],x]

You should get an error that looks like the one below:

The student tells you that they have tried using Clear[y] and then replacing the ‘=’ with a double equals ‘==’ but it still didn’t work and got the following error:

What command would have succesfully removed any definition from y allowing the student to?

Use this command to remove the definition of y and then correct the students code for the differential equation so it runs succesfully.