How do you use the Quadratic Formula to solve First Order ODE?

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SUMMARY

The discussion focuses on applying the Quadratic Formula to solve a First Order Ordinary Differential Equation (ODE). The user is tasked with expressing y in terms of t after integrating both sides of the equation. Key advice includes treating the term t² + k as a constant to form a standard quadratic equation, allowing for the application of the Quadratic Formula to find solutions. This method is essential for transforming the integrated equation into a solvable format.

PREREQUISITES
  • Understanding of First Order Ordinary Differential Equations (ODEs)
  • Familiarity with the Quadratic Formula
  • Basic integration techniques
  • Knowledge of algebraic manipulation of equations
NEXT STEPS
  • Study the application of the Quadratic Formula in various mathematical contexts
  • Explore advanced techniques for solving First Order ODEs
  • Learn about integrating factors in ODEs
  • Review examples of quadratic equations derived from differential equations
USEFUL FOR

Students studying differential equations, mathematics educators, and anyone seeking to understand the application of the Quadratic Formula in solving ODEs.

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Homework Statement



How do you use the Quadratic Formula to solve First Order ODE?

For example, I am given this integration (see attachment at the bottom).

Homework Equations


The Attempt at a Solution



I integrated both sides but I do not know where to go from there (see attachment at the bottom). My goal is to express y in terms of t. Furthermore, my book says I should use the Quadratic Formula to figure it out. I know what the Quadratic Formula is, but I do not know how to apply it in this situation. Can anyone give me any hints? Thanks.
 

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Treat the t^2 + k as any other constant. Bring it over and you have a quadratic equation like any other.
 
Sethric said:
Treat the t^2 + k as any other constant. Bring it over and you have a quadratic equation like any other.

I see. Thanks.
 

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