Diff Equation with one solution?

  • Thread starter >Modx<
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In summary, the question is to provide a differential equation that has only a trivial solution, y = 0. The attempted solution is y' = y, but this also has a non-trivial solution of y = e^x. The suggestion is to use y' = y with the boundary condition y(0) = 0, which only has one solution. The question is now considered solved with the help of Mark44 and CompuChip.
  • #1
>Modx<
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Homework Statement



Hi guys, my question is from a book on differential equation. It asks me to give a differential equation that has only a trivial solution, y = 0.

Homework Equations





The Attempt at a Solution



I give it some thought and I can only think of a diff eq'n of y' = y, however, in this case y = e^x will also be a valid solution but not a trivial one. So I am not so sure if this is what the question wants, or there is a diff eq'n that has only one solution which is y =0. Thank you in advance.
 
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  • #2
Well, you said "y = 0", isn't that a valid answer?
If you insist that it contains derivatives of higher order than 0, you can easily adapt it (but you need boundary conditions).
 
  • #3
y' = y; y(0) = 0
This initial-value problem has only one solution.
 
  • #4
Oh ok ... that will do ... Thank you Mark44 and CompuChip.
 

1. What is a differential equation with one solution?

A differential equation with one solution is an equation that can be solved to find a single unique function or curve that satisfies the equation. It is a type of differential equation that has only one possible solution.

2. How is a differential equation with one solution different from other types of differential equations?

A differential equation with one solution is different from other types of differential equations because it has a unique solution, whereas other types may have multiple solutions or no solutions at all.

3. What are some real-world applications of differential equations with one solution?

Differential equations with one solution are used in many fields of science and engineering to model and analyze various phenomena such as population growth, chemical reactions, and electrical circuits. They are also used in physics and economics to describe motion and predict future trends.

4. How are differential equations with one solution solved?

Differential equations with one solution are typically solved using various mathematical techniques, such as separation of variables, substitution, and the method of undetermined coefficients. These methods involve manipulating the equation to isolate the dependent variable and then finding a function that satisfies the equation.

5. Are there any limitations to using differential equations with one solution?

Yes, there are some limitations to using differential equations with one solution. These equations may not be able to accurately model complex systems or phenomena with multiple variables. Additionally, the solutions obtained may only be approximate and may not precisely match the real-world data. In some cases, numerical methods may be needed to solve these equations.

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