General Solution for dy/dt=2ty+4e^(t^2)

In summary, a general solution is a mathematical formula or equation that represents all possible solutions to a problem or set of equations. It differs from a particular solution, which is a specific solution with values for variables. A general solution is needed when there are multiple solutions or when trying to find a pattern or trend. To find a general solution, algebraic methods or visual aids such as graphs can be used. It is important because it allows for a deeper understanding and analysis of a problem, and can also be used to find specific solutions.
  • #1
stasianlov
1
0
find general solution for differential equation dy/dt=2ty+4e^(t^2)

i got e^(t^2)(4t+k) is that right?
 
Physics news on Phys.org
  • #2
hi stasianlov! :smile:

(try using the X2 button just above the Reply box :wink:)
stasianlov said:
find general solution for differential equation dy/dt=2ty+4e^(t^2)

i got e^(t^2)(4t+k) is that right?

yes that's fine :smile:

what is worrying you about that? :confused:
 
  • #3
you can check the answer by substituting the solution y(t) and its derivative dy/dt in the differential equation. The results should be 0.
 

1. What is a general solution?

A general solution is a mathematical formula or equation that represents all possible solutions to a problem or set of equations. It is not a specific solution, but rather a set of solutions that can be obtained by plugging in different values for variables.

2. How is a general solution different from a particular solution?

A particular solution is a specific solution to a problem or set of equations, while a general solution represents all possible solutions. A particular solution will have specific values for variables, while a general solution will have variables that can be replaced with different values to obtain different solutions.

3. When do you need to find a general solution?

A general solution is needed when there are multiple solutions to a problem or set of equations. It is also useful when trying to find a pattern or trend in a set of data.

4. How do you find a general solution?

To find a general solution, you need to solve the problem or set of equations using algebraic methods, such as substitution or elimination. This will result in a formula or equation with variables that represent all possible solutions. You can also use graphs or tables to find a general solution by identifying patterns.

5. Why is finding a general solution important?

Finding a general solution is important because it allows us to understand and analyze a problem or set of equations more comprehensively. It also helps us to find all possible solutions and identify patterns or trends that may not be evident when only looking at a particular solution. Additionally, a general solution can be used to find specific solutions by plugging in values for variables.

Similar threads

  • Differential Equations
Replies
3
Views
2K
  • Differential Equations
Replies
8
Views
2K
Replies
3
Views
740
  • Differential Equations
Replies
16
Views
818
  • Differential Equations
Replies
3
Views
1K
  • Differential Equations
Replies
7
Views
1K
  • Differential Equations
Replies
6
Views
2K
  • Differential Equations
Replies
7
Views
3K
  • Differential Equations
Replies
7
Views
1K
Replies
1
Views
3K
Back
Top