Differential Equation second degree help

Click For Summary
SUMMARY

The discussion focuses on solving the second-degree differential equation \(\frac{dy}{dx} = y^2 + 1\). The solution involves dividing both sides by \(y^2 + 1\) and then multiplying by \(dx\), making it integrable. The participant expresses initial confusion but successfully resolves the problem with guidance, highlighting the importance of remembering inverse trigonometric derivatives in the process.

PREREQUISITES
  • Understanding of differential equations, specifically second-degree equations.
  • Familiarity with integration techniques.
  • Knowledge of inverse trigonometric functions and their derivatives.
  • Basic algebraic manipulation skills.
NEXT STEPS
  • Study the method of separation of variables in differential equations.
  • Learn about integrating functions involving inverse trigonometric derivatives.
  • Explore applications of second-degree differential equations in real-world scenarios.
  • Practice solving various types of differential equations to build confidence.
USEFUL FOR

Students studying calculus, particularly those learning about differential equations, as well as educators looking for effective teaching strategies for complex mathematical concepts.

kristo
Messages
12
Reaction score
0

Homework Statement


\frac{dy}{dx}= y^2 + 1


Homework Equations





The Attempt at a Solution


I have no idea how to go about it. I've never solved a differential equation of second degree before.
 
Physics news on Phys.org
It may look scary, but it really isn't. Just divide both sides by (y2+1) then multiply both sides by dx. It's integrable from there.
 
Thanks a lot, I got it now. I keep forgetting the inverse trig derivatives.
 
No problem at all.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
2K
Replies
3
Views
2K
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
17
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K