1. ## Linear ODE problem

Hi, I am supposed to solve the linear ODE:

x(dy/dx) + 2y = (sin x) / x , y(2) = 1

Can anyone help me get started with this? I am at a loss for anything relevant.

2. Originally Posted by thecelticswin
Hi, I am supposed to solve the linear ODE:

x(dy/dx) + 2y = (sin x) / x , y(2) = 1

Can anyone help me get started with this? I am at a loss for anything relevant.
do you mean $y' = \frac {x^3 - 2y}x$ ?? ....hey! you changed the question!

so you have $xy' +2y = \frac {\sin x}x$

divide through by $x$, we get

$y' + \frac 2xy = \frac {\sin x}{x^2}$

now solve using the integrating factor method

3. got it, it's even easier if you multiply through by x squared. (integrating factor is just x squared then!) thanks!

4. Originally Posted by thecelticswin
got it, it's even easier if you multiply through by x squared. (integrating factor is just x squared then!) thanks!
right. i didn't know if you would catch that though, so i wanted to go by the book. sometimes you make such leaps in logic and students get lost and bewildered