Well, i realy i am pissed at the moment because of this. I have been trying to figure out if there is a proof/justifaction for the method of variation of parameters and have had absolutly no luck. I have searched the internet and almost every differential equation books in my university library and none of the book give much of an explanation of the this method other than how to turn the crank and mysteriously solve equation using this method. The source of my anger is this. it seems to me that most math books dont give explaination of why certain forumulas/method of solution actualy work, just how to use them. I dont know about everyone else but to me this is abosolutly pointless. I learn nothing at all from this. So my questions are the following: 1) can someone point my to a resource that will explain why this method works. Please! 2) Is it just me being slightly sleep derprived/angry/bitter/undersexed/undertalented or do i have a point about math books not realy focucing on why certian formulas and/or methods of solution work. To be fair one book i found "derrick & grossman first course in differential equation" did at least try to explain the method but i dont follow it. Here is an example of what the text says "To use this method it is necessary to know the general solution c1y1(x) + c2y2(x) of the homogenous equation y'' + a(x)y' + b(x)y = 0" ...... ummm why? and another thing the text says "Lagrange noticed that any particular solution yp of (1) must have the property that yp/y1 and yp/y2 are not constants, suggesting that we look for a particuylar solution of (1) of the form y(x) = c1(x)y1(x) + c2(x)y2(x)"...... ummm i dont see why this would suggestion that particular solution. Please physics forms your my only hope. i think i need a nap.