How Do You Solve the Differential Equation dy/dt + (1/t)y = t*exp(-2t)?

In summary, a general solution question is a type of problem that requires finding a solution that satisfies all possible cases or scenarios. It is different from a specific solution, which only works for a particular case. General solutions should be used when dealing with complex problems or when a specific solution is not known. They can save time and effort, but may not always be as precise as a specific solution. However, finding a general solution may require more advanced problem-solving skills and may not be possible for every problem.
  • #1
Eggmans
2
0
Compute the general solution of the differential equation?

dy/dt+1/t y = t*exp(-2t)

y is outside 1/t


can't seem to get it
 
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  • #2
Find the integrating factor for the left hand side.

d/dt (some function * y) = ...
 
  • #3
d(u(t)y)/dt= u(t)y'+ u'(t)y and you want that equal to u(t)y'+ (u(t)/t)y. That gives a simple separable equation for the integrating factor, u.

By the way, simpler than saying "y is outside 1/t" is to use parentheses: (1/t)y
 

FAQ: How Do You Solve the Differential Equation dy/dt + (1/t)y = t*exp(-2t)?

What is a general solution question?

A general solution question is a type of problem that requires finding a solution that satisfies all possible cases or scenarios. It is often used in mathematics and science to find a solution that works for a wide range of situations.

How is a general solution different from a specific solution?

A specific solution is a solution that only works for a particular case or scenario, while a general solution works for all possible cases. A specific solution is often more precise and specific, while a general solution is more broad and versatile.

When should I use a general solution?

A general solution should be used when the problem requires finding a solution that works for all possible cases. This can be useful when dealing with complex problems or when a specific solution may not be known or applicable.

What are the benefits of using a general solution?

Using a general solution can save time and effort, as it eliminates the need to find multiple specific solutions for different cases. It also allows for a more comprehensive and versatile approach to problem-solving.

Are there any limitations to using a general solution?

One limitation of using a general solution is that it may not be as precise or accurate as a specific solution. Additionally, finding a general solution may require more advanced problem-solving skills and may not always be possible for every problem.

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