Question

Solve the DE: y'+(2x-1)y=4x-2

Answer 1

I got the answer

\[y=2+\frac{ce^x}{e^{x^2}}\]

Answer 2

it can be simplified more i guess

Answer 3

\[ \huge y = e^{-\int (2x-1)dx} \times \int (4x-2)e^{\int (2x-1)dx} dx + \\
\huge Ce^{-\int (2x-1)dx}\]

Answer 4

that's what i did where'd the - come from though

Answer 5

for the first integral and last?

Answer 6

the integrals equal

\[e^{x^2-x}\]

Answer 7

i can't remember the property of base e is it


\[e^{a^b}=e^{a*b}\]

Answer 8

if that is the case then it can be simplified more

Answer 9

Oh ... there's a whole lecture series discussing how to solve this type of equation here
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/

Answer 10

did you ever get an answer? that was my personal answer... i needed a check lol

Answer 11

it really isn't as base as it looks because the x^2-x when used as a u will get u du=(2x-1)dx

Answer 12

bad* as it looks

Answer 13

seems you are right
http://www.wolframalpha.com/input/?i=y%27+%2B+%282x-1%29y+%3D+4x-2

Answer 14

thanks

Answer 15

yw