How Do You Solve This Second-Order Linear Differential Equation?

  • Thread starter Thread starter fan_103
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on solving the second-order linear differential equation represented by x²(d²y/dx²) + 3x(dy/dx) + 5y = 3x. A key suggestion for solving this equation is to use the substitution x = e^z, which simplifies the problem. The participants emphasize the importance of understanding the general form of second-order linear differential equations and the methods to approach them, particularly for those who are new to the topic.

PREREQUISITES
  • Understanding of second-order linear differential equations
  • Familiarity with differential calculus
  • Knowledge of substitution methods in differential equations
  • Basic grasp of exponential functions
NEXT STEPS
  • Research methods for solving second-order linear differential equations
  • Learn about the substitution technique x = e^z in differential equations
  • Explore the general solution of linear differential equations
  • Study specific examples of second-order linear differential equations and their solutions
USEFUL FOR

Students studying differential equations, educators teaching advanced calculus, and anyone seeking to enhance their problem-solving skills in mathematical analysis.

fan_103
Messages
24
Reaction score
0
x^2d^2y/dx^2+3xdy/dx+5y=3x
I don't know where to start with the question ,can anyone here help me pleasez.
 
Last edited:
Physics news on Phys.org
Do you know how to solve x^2 y'' + axy' + by =0 in general?

Hint: Use the substitution x = e^z
 
Thanks for the help much appreciated..I have not yet done this chapter.
 

Similar threads

  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 14 ·
Replies
14
Views
1K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 18 ·
Replies
18
Views
3K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
2K
Replies
9
Views
2K