1. ## Differential Equation

Hey

Im trying to solve the following differential equation.

$x*dy/dx +y = e^(-x)$ <--- e (to the power of) -x

But I can't rearrange the equation to get the x's on the left handside and the y's on the right hand side

Thanks a million

Eddie

2. $
xy'+y=e^{-x}.$

This is a linear ODE, but instead to find the integrating factor, we can see that $xy'+y=(x\cdot y)'=e^{-x}\implies xy=\int e^{-x}\,dx.$

Can you take it from there?

3. Im not really familar with linear DE's

y=x(-(1/x*e^x))+(c/x)

Am i on the right track?

4. I don't get very well what you wrote, but the answer is $y(x)=\frac{k-e^{-x}}x.$

5. Ok think I'm doing it wrong could you please show me your working ? Would help me heaps

Much Appreciated

Eddie

6. Since $\int e^{-x}\,dx=-e^{-x}+k,$

$xy=-e^{-x}+k,$ and the conclusion follows.

7. Hey again

I dont quiet understand what you did? This basically what Im doing.

x*(dy/dx) + y = e^-x

d(xy)/dx = e^-x

d(xy) = (e^-x) dx

xy = -e^-x + c

y = (1/x)*(-e^-x + c)

Is this right? if not where am I going wrong?

8. It is correct, it's just that on post #3 I didn't understand the notation.