## Practice exam for First Midterm

This is a practice exam for the first midterm. Feel free to drop any comment or question below. I will try to answer here as many as possible, until the day before the exam. This is a good opportunity to compare notes and work with other students. Enjoy!

- Prove that the function is a solution of the equation and find the particular solution satisfying
- Apply both Euler and Improved Euler methods to solving numerically the differential equation with initial condition in the interval Use a time-step Prepare a table showing four-decimal-place values of the approximate solution and the actual solution at the points
- Find the general solution of the equation
- Find the particular solution of the equation that satisfies the initial condition
- Find the equation of a curve that goes through the point and satisfies that the slope at any of its points is equal to three plus the coordinate at that point.
- Find the general solution of the equation
- Find the general solution of the equation
- Find the general solution of the equation
- Find the general solution of the equation
- Find the general solution of the equation
- Find the general solution of the second-order differential equation
- Find the particular solution to the equation that satisfies the initial conditions and
- And let’s finish with a nice punch-line: Find the general solution of the equation If you are able to get this question in less than 30 minutes without the help of a computer, and explain to someone else step-by-step how to do it, I consider that you have mastered the material of the first midterm.

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how can you find the actual solutions to problem 2?

You will have to solve the differential equation (use “jazz” for this one), get the particular solution that satisfies and plug the values of

for number 12. I’ve gotten to dy/dx = sqrt(y^4 +c) assuming that is correct, I’m not sure where to go from there, it seemed separable but was having some trouble with that.

For number 2 is the solution y=2+x-e^x if yes, why do I get answers that are way different than the ones I got from using Eulers method?

If you got similar answers for both EM’s then that means your solution is wrong.

is the answer to number 5 : y’=(y-1)/x?

for number 5 i got y=e^x – 3