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(Solved): Please help me I am really confused about dy/dx=dv/dx-1, how is this equation come
h) (x+y)dx+(3x ...
Please help me I am really confused about dy/dx=dv/dx-1, how is this equation come
h) (x+y)dx+(3x+3y?4)dy=0. (Hint: Use the substitution v=x+y.) Note that ?y?M??=?x?N?, so this equation is not exact. First note that if v=x+y, then y=v?x and dxdy?=dxdv??1. Rewrite the equation as v+(3v?4)dxdy?v+(3v?4)(dxdv??1)dxdv?2v?43v?4?dxdv?(23?+2u?42?)dv?=0=0=3v?42v?4?=1=dx? using polynomial long division or some other rearranging. Integrating, we have 23?v+ln?2v?4?=x+C23?(x+y)+ln?2(x+y)?4?=x+C?