Is this the general solution for the DE y''+4y' +20y=0 with initial conditions?

  • Thread starter RadiationX
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In summary, D.E. soulution is a method used to solve differential equations in mathematics and physics. It involves using mathematical techniques to find a function or set of functions that satisfy a given differential equation. This method has many applications in various fields, including physics, engineering, economics, and biology. While it may initially seem difficult to learn, with practice and understanding of the underlying principles, it can be mastered. However, there are limitations to D.E. soulution, as it may not always provide an exact solution and some equations may not have a closed-form solution at all.
  • #1
RadiationX
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solve [tex]y''+4y' +20y=0 ;y(0)=-3 ,\\ y'(0)=5[/tex] is this the general solution?

[tex]e^{-2t}(C_1\cos{4t} + C_2\sin{4t})[/tex]
 
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  • #2
Yes. It is.
 
  • #3
You don't need the general solution as the final answer,but the particular solution.

Daniel.
 

FAQ: Is this the general solution for the DE y''+4y' +20y=0 with initial conditions?

1. What is D.E. soulution?

D.E. soulution stands for Differential Equation Solution, which is a method used to solve differential equations in mathematics and physics.

2. How does D.E. soulution work?

D.E. soulution involves using mathematical techniques to find a function or set of functions that satisfy a given differential equation. This can involve techniques such as separation of variables, substitution, and integration.

3. What are some applications of D.E. soulution?

D.E. soulution has many applications in various fields, including physics, engineering, economics, and biology. It is used to model and predict the behavior of systems that can be described by differential equations.

4. Is D.E. soulution difficult to learn?

Like any mathematical concept, D.E. soulution may seem difficult at first, but with practice and understanding of the underlying principles, it can be mastered. It is important to have a strong foundation in calculus and algebra to understand D.E. soulution.

5. Are there any limitations to D.E. soulution?

D.E. soulution may not always provide an exact solution to a differential equation, especially for more complex equations. In some cases, numerical methods may need to be used to approximate a solution. Additionally, some differential equations may not have a closed-form solution at all.

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