Thread: dy/dx=e^(-x^2) - 2xy subject to y(2)=0

hi,
need some help for this question, i tried solving by seperating dy to one side and dx to the other and integrating however dont get the right answer...how can i solve this
any help much appreciated

solve the following differential equation for y giving answer in form y=f(x)

dy/dx=e^(-x^2) - 2xy subject to y(2)=0

thankyou

The equation is linear in y, so use the integrating factor approach. What do you get?

i used the integrating factor method
integrating factor being e^(x^2)
i got the answer to be y=2/(e^(x^2))

but the answer book shows the answer to be
y = (x-2)e^(-x^2)


thankyou for your quick reply

Originally Posted by metalkakkarot

i used the integrating factor method
integrating factor being e^(x^2)

That is correct.

i got the answer to be y=2/(e^(x^2))

but the answer book shows the answer to be
y = (x-2)e^(-x^2)


thankyou for your quick reply

The book is correct. How did you get your answer? Can you please show the steps?

sorry for delayed reply had to upload the photo from my mobile..
i did the question again and essentially had forgotten to integrate the RHS first time round...
now i get close to the correct answer except a sign difference...
at the end i subbed y=2 and x=0 to get c=2

Your working is correct up to the determination of the arbitrary constant. If you plug in x = 2, do you get y = 0? (I suspect you may have reversed the roles of x and y, perhaps?)

thankyou so much...it was as you said i had switched the x and the y and the end....got the answer

+thanks

You're very welcome. Have a good one!