Find Solution of DE: dy/dx+(1/x)y=1/x^2

  • Thread starter Eastonc2
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In summary, the conversation is about finding the general solution of a given differential equation, with the use of an integrating factor. After putting the integrating factor into the equation, the person is unable to progress further due to difficulty with the right side of the equation. Eventually, they realize that e^lnx simplifies to x and they consider their previous attempts a waste of time.
  • #1
Eastonc2
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Homework Statement


find the general solution of the given DE
dy/dx+(1/x)y=1/x^2


Homework Equations


integrating factor (e^(∫P(x)dx)=e^(lnx)


The Attempt at a Solution


so i put my integrating factor into the equation, and get:

e^(lnx)(dy/dx)+(e^(lnx)/x)y=e^(lnx)/x^2
and can't progress any further. of course, I can integrate the left side of the equation, which leaves me with e^(lnx)y, but the right side is really throwing me for a loop. are there any suggestions out there?
 
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  • #2
ok, so it must be getting a little too late for my brain. e^lnx is...x
so this was a major waste of time/space
 

FAQ: Find Solution of DE: dy/dx+(1/x)y=1/x^2

1. What is a differential equation (DE)?

A differential equation is an equation that involves an unknown function and its derivatives. It describes how a quantity changes over time or space and is often used to model real-world phenomena in various fields of science and engineering.

2. How do you solve a differential equation?

To solve a differential equation, you need to find the unknown function that satisfies the equation. This can be done by using various techniques such as separation of variables, integration, or by using specific methods for different types of differential equations.

3. What is the general solution of a differential equation?

The general solution of a differential equation is a family of solutions that contains all possible solutions to the equation. It usually contains one or more arbitrary constants that can be determined by applying initial conditions or boundary conditions.

4. How do you find the particular solution of a differential equation?

The particular solution of a differential equation is a specific solution that satisfies the equation and also satisfies any given initial or boundary conditions. It can be found by substituting the given conditions into the general solution and solving for the arbitrary constants.

5. How can you apply differential equations in real life?

Differential equations are used to model and understand various real-world phenomena such as population growth, heat transfer, fluid flow, and electrical circuits. They are also used in fields such as physics, chemistry, biology, economics, and engineering to make predictions and solve problems.

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