Initial Value Problem/Separable Equation

• Mar 17th 2013, 11:04 AM
RobertXIV
Initial Value Problem/Separable Equation
So in this problem we are given that
(xlnx)y' + y = x^2 * e^x
and
y(e) = 1

I under stand how it needs to be solved (need to get all y on one side, all x on other side, then integrate, then solve for y, then sub in y(e) = 1 to determine value of C.
I can only get this far, however:
dy/dx = (x^2 * e^x)/xlnx + y/xlnx

I could factor out the 1/xlnx, but it wouldn't be separable. I could do some minor simplifying, but then it wouldn't be factorable.

Any help is greatly appreciated :)
• Mar 17th 2013, 11:18 AM
MINOANMAN
Re: Initial Value Problem/Separable Equation
Robert

The D.E you mentioned is not separable ....it has the type dy/dx+a(x)y=b(x)
where a(x) and b(x) are functions of x. This type of D.E is linear D.E first order...and cannot be solved by separating the variables...

consult your book about the linear D.E of first order and see how you can solve it ....IT IS EASY.

MINOAS
• Mar 17th 2013, 11:56 AM
RobertXIV
Re: Initial Value Problem/Separable Equation
My Lord! I remember that now.
How silly of me ahahaha thanks a lot!