The problem is "solve equation:"
(x+y)dy + (x-y)dx =0
I rearanged it to look like:
dy/dx = (y-x)/(x+y)
What's the next step???
THANKS !! Explanation + answer gets 10 points :)
(x+y)dy + (x-y)dx =0
I rearanged it to look like:
dy/dx = (y-x)/(x+y)
What's the next step???
THANKS !! Explanation + answer gets 10 points :)
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Change variable from y to z where y=zx, dy/dx=(dz/dx)x+z so
xdz/dx+z = (zx-x)/(x+zx)=(z-1)/(1+z) so
xdz/dx=(z-1)/(1+z) - z=-(1+z^2)/(1+z) and separating the variables
gives (1+z)/(1+z^2) dz +(1/x) dx=0 and integrate to give
tan^-1(z)+(1/2)ln(1+z^2) = C and replace z by y/x
tan^-1(y/x)+(1/2)ln(1+ y^2/x^2) =C
You could try the change of variable from y to z given by y=x/z if you like.
xdz/dx+z = (zx-x)/(x+zx)=(z-1)/(1+z) so
xdz/dx=(z-1)/(1+z) - z=-(1+z^2)/(1+z) and separating the variables
gives (1+z)/(1+z^2) dz +(1/x) dx=0 and integrate to give
tan^-1(z)+(1/2)ln(1+z^2) = C and replace z by y/x
tan^-1(y/x)+(1/2)ln(1+ y^2/x^2) =C
You could try the change of variable from y to z given by y=x/z if you like.