Solutions for Differential Equations Homework

[Gale]

So I'm wondering if anyone knows a way i can find answers to my homework before i hand it in. sometimes I'm not sure if I'm doing it right, and i want to check my final result. obviously i still have to show my work, so just having an answer doesn't get my homework done for me. there's selected answers in the back, but basically only one per problem 'type' so if i get stuck on that one, even if i eventually get the right answer, I'm still not confident i can do the rest very well. sometimes i'll google problems with a little luck, but usually that doesn't work super well. Specifically, right now I'm doing some differential equations work, and each problem is a lot of math and I'm not sure if my answers look right. I keep getting very wrong answers on a few, (doesn't fit the 'protoype' diff eq that I'm working on) and so I'm afraid I've done most of them wrong.

any ideas?

 

[AKG]

Sometimes you can hunt around the internet for solutions to problems in a textbook. For example, somtimes some university will have a course that uses a specific textbook, and the TA might post a bunch of the solutions on the web for the students to reference. If you happen to be using the same book, then something like this would help. I know Spivak's Calculus on Manifolds has solutions like this on the web somewhere, and Munkres' Topology too, but not solutions to all problems.

You can also compare answers with others in your class. And finally, you can post your solutions here and ask if you've done them correctly.

 

[t!m]

Your best bet is probably a computer program capable of analytically solving differential equations. I believe even a TI-89 can do this. I've used mine on multiple occasions to check my answer.

 

[JasonRox]

Your best bet is probably a computer program capable of analytically solving differential equations. I believe even a TI-89 can do this. I've used mine on multiple occasions to check my answer.

A programmable calculator is your best bet.

You know it's going to be a good approximation. Since you say your answers are far off sometimes, then if it is far off the approximation, then clearly it's wrong. If it's close, it's all good or atleast you won't worry so much.

 

[Speedo]

Google the name of your textbook and author, sometimes you get lucky. We managed to find another school using our book where the prof had posted parts of the solutions guide.

It's also worth checking out the website of the author or publisher. In the case of the calculus book I've used the publisher has a great website that includes free, step-by-step solutions to every odd homework problem in the book.

 

[Hurkyl]

Many problems come with an easy way to check your answers -- simply plug your answer into the equation to see if it works. This works fine when solving differential equations.

Sometimes you need a little more creativity. Solving an integral? Differentiate your answer and see if you get the integrand. Differentiating a function? Compare it to an estimate using [f(x+h)-f(x)]/h for a very small h.

Another thing that's often useful is to simply put your work aside and do the problem again from scratch. Many silly mistakes can be detected this way: e.g. it's uncommon to make the same sign mistake twice. (Though this doesn't catch a systematic conceptual error)