All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
Look Ma, no integrals! (Posted on 2006-05-02) Difficulty: 3 of 5
The professor wrote the differential equation f²/f'=1 on the blackboard, and asked the students to solve it.

Everybody started working with the usual methods, except for a kid at the back of the class, who happened to have skipped that material, but was very bright.

Can you solve this equation without any integration?

See The Solution Submitted by Federico Kereki    
Rating: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Worked it out | Comment 13 of 14 |
Let's write [a0, a1, a2, a3...] as short for f(x)= a0 + a1.x + a2.x^2 + a3.x^3 + ....

Then f ' = [a1, 2.a2, 3.a3, 4.a4...] and f^2 = [a0^2, 2.a0.a1, a1^2+2.a0.a2, 2.a1.a3+2.a0.a4, ...]

Equating f ' and f^2 we get

a1 = a0^2
2.a2 = 2.a0.a1 = 2.a0^3, so a2 = a0^3
3.a3 = a1^2+2.a0.a2 = 3.a0^4, so a3 = a0^4
4.a4 = 2.a1.a3+2.a0.a4 = 4.a0^5, so a4 = a0^5

and then f=[a0, a0^2, a0^3, a0^4...]

Writing just "a" instead of a0, f(x)=a/(1-ax).

  Posted by e.g. on 2006-05-04 09:33:36
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information