- #1
thomas49th
- 655
- 0
Homework Statement
[tex]\frac{dy}{dx} + \frac{y}{2x} = -x^{\frac{1}{2}}[/tex]
Homework Equations
[tex]yT =\int{QT}dx + C[/tex]
where T is the intergrating factor
T = [tex]e^{\int{P}dx[/tex]
and P is the co-efficient of y from the differential equations
The Attempt at a Solution
well to find T we need to do:
[tex]e^{\int{\frac{1}{2x}}}dx[/tex]
[tex]e^{\frac{1}{2}\int{\frac{1}{x}}}dx[/tex]
[tex]e^{\frac{1}{2}ln|x|}[/tex]
[tex] = x^{\frac{1}{2}}[/tex]
so using [tex]yT =\int{QT}dx + C[/tex]
you get
[tex] yx^{\frac{1}{2}}= \int{x^{\frac{1}{2}x^-{\frac{1}{2}}}dx[/tex]
[tex] yx^{\frac{1}{2}}= \int{1}dx[/tex]
[tex] yx^{\frac{1}{2}}= x + c[/tex]
the answer in the back of the book says [tex]yx^{\frac{1}{2}} = \frac{1}{2}x^{2}[/tex]
Where have I gone wrong?
Thanks :)