Differential Equations Question

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SUMMARY

This discussion focuses on matching differential equations with their corresponding solutions in an Ordinary Differential Equations (ODE) course. The equations provided include both second-order linear homogeneous equations and a non-homogeneous equation. The suggested approach for solving the problem involves calculating the first and second derivatives of the proposed solutions and substituting them into the differential equations to verify matches. This method is essential for students who have only covered first-order linear and separable ODEs.

PREREQUISITES
  • Understanding of Ordinary Differential Equations (ODEs)
  • Knowledge of first-order linear and homogeneous ODEs
  • Ability to compute first and second derivatives
  • Familiarity with the concept of matching solutions to differential equations
NEXT STEPS
  • Study second-order linear differential equations and their solutions
  • Learn how to compute derivatives of functions
  • Explore methods for solving homogeneous and non-homogeneous ODEs
  • Practice matching differential equations with solutions using substitution techniques
USEFUL FOR

Students enrolled in ODE courses, particularly those beginning their study of second-order differential equations, and educators looking for effective teaching strategies in this area.

MeMoses
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Homework Statement


Match each of the differential equations with a solution from the list below.
1. 2x^2 * y'' + 3xy' = y
2. y'' + 12y' + 36y = 0
3. y'' - 12y' + 36y = 0
4. y'' + y = 0

And then the possible solutions A-D


Homework Equations





The Attempt at a Solution


This is from a web assignment from a ODE course which just started. We have only cover first order linear, homogenous ODE's and vairable seperable. I have no idea where to start here. Am I just overlooking something? Do I need to work backwards from the solutions? Any help to get me started would be greatly appreciated.
 
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MeMoses said:

Homework Statement


Match each of the differential equations with a solution from the list below.
1. 2x^2 * y'' + 3xy' = y
2. y'' + 12y' + 36y = 0
3. y'' - 12y' + 36y = 0
4. y'' + y = 0

And then the possible solutions A-D


Homework Equations





The Attempt at a Solution


This is from a web assignment from a ODE course which just started. We have only cover first order linear, homogenous ODE's and vairable seperable. I have no idea where to start here. Am I just overlooking something? Do I need to work backwards from the solutions? Any help to get me started would be greatly appreciated.

If you haven't done anything with 2nd order DEs yet, probably the best course of action is find the 1st and 2nd derivatives of the solutions you are given, and substitute them into each of the four given differential equations.
 

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