Thread: First order differential and linear equations

Hello guys,

I need help with two of the most weird equations i have ever seen.

Problem 1:
Solve the initial value problem

xy' + 3y = x^7, y'(0) = 3.

Problem 2:
Solve the initial value problem

(x^2)y' + y = 1, y(1) = 2.


Thanks, in advance.

Originally Posted by tapiaghector

Hello guys,

I need help with two of the most weird equations i have ever seen.

Problem 1:
Solve the initial value problem

xy' + 3y = x^7, y'(0) = 3.

These quations aren't very weird at all. You need to use the integrating factor method for both. They just need a little re-arranging first.



divide both sides by x



Then follow the steps in this post

http://www.mathhelpforum.com/math-he...equations.html

hey thanks my friend, i have another question, how do you evaluate y'(0) = 3?

Originally Posted by tapiaghector

hey thanks my friend, i have another question, how do you evaluate y'(0) = 3?

After you've found your general solution you differentiate it. Then you substitute x = 0 and equate the result to 3. Then you solve for your arbitrary constant of integration.

Originally Posted by tapiaghector

hey thanks my friend, i have another question, how do you evaluate y'(0) = 3?

This is to be evaluated after you have a general solution.

What is your general solution?

I have something along the lines of



You will need to apply integration by parts from here.