Find the particular solution to the differential equation

[nkdfnkn]

Find the particular solution to the differential equation y′−  y(x)/x = -xe^-x...........with the condition  y  =  2 when x  =  1.

 

[Deleted member 4993]

Find the particular solution to the differential equation y′−  y(x)/x = -xe^-x...........with the condition  y  =  2 when x  =  1.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this assignment.

 

[nkdfnkn]

Sorry, I'm completely stuck. I don't know where to begin

 

[MarkFL]

Hint: Divide through by \(x\) to get:

[MATH]\frac{1}{x}y'-\frac{1}{x^2}y=-e^{x}[/MATH]
Now you should recognize that the LHS can be expressed as the derivative of a product.

 

[LCKurtz]

And although MarkFL noticed it by inspection, you should recognize the equation is a first order linear DE for which the integrating factor method is appropriate. Your integrating factor is [MATH]R(x) = e^{\int -\frac 1 x~dx} = x^{-1}[/MATH], which gives Mark's equation.

 

[HallsofIvy]

Sorry, I'm completely stuck. I don't know where to begin

Then I recommend you begin by taking an introductory differential equation course!