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

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To solve a first-order ordinary differential equation (ODE) using the Quadratic Formula, first integrate both sides of the equation. After integration, rearrange the equation to form a standard quadratic equation. Treat the term t^2 + k as a constant when applying the Quadratic Formula. This approach allows for expressing y in terms of t effectively. Understanding how to manipulate the equation is key to finding the solution.
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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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