Question

I am having trouble with this problem. I cannot get the answer in the back of the book. y'=(x+y)/(2x)

Answer 1

solve the homogeneous equation

Answer 2

nonlinear

Answer 3

you can rewrite the equation in this way
\[y'=\frac{ x(1+\frac{ y }{ x })0 }{ 2x }=\frac{ 1+\frac{ y }{ x } }{ 2 }\]

Answer 4

without the zero there , missclicked

Answer 5

now u can set \[u=\frac{ y }{ x }=>y=ux=>y'=u'x+u\]

Answer 6

so now just substitude for y' and for u

Answer 7

that what I have been doing and I get \[\frac{ (x-y)^{2} }{ (x)^{3} }=c\]

Answer 8

hm i assume u have some mistake

Answer 9

I do not know what I did wrong. I keep getting the same answer.

Answer 10

ok i tell u what i get , i get smt like \[x-constant*\sqrt{x}=y\]

Answer 11

did you get to the point where u should find integrals of this
\[\int\limits_{}^{}{\frac{ dx }{ x }}=\int\limits_{}^{}{\frac{ 2du }{ 1-u }}\]

Answer 12

yep

Answer 13

so what did u get for the integrals?

Answer 14

\[\ln x +C=2\ln (1-v)\]

Answer 15

ok seems like you forgot a "-" sign in front of 2ln(1-u)

Answer 16

oh that it. this problem has been troubling me for hours. Such I stupid Mistake. Thanks a lot!

Answer 17

did u get right answer now ? :D and yeah such a shame losing so much time at just a - sign xD

Answer 18

yea I got the right answer.

Answer 19

cute , good luck ^^