I was stuck at numbers 2 and 6. This is a linear ODE. 2.(y+1)dx+(4x−y)dy=0 Divided it by dx: (y+1)+(4x−y)dydx=0 Transposed the (y+1) (4x−y)dydx=−(y+1) Divided it by (4x−y) dydx=2y(x−3) The farthest I can go is: dxdy=(2x3x2)−(6y3x3). The rest of the problems were easily solved but those 2 are very hard to bring to the standard form.

Question

I was stuck at numbers 2 and 6. This is a linear ODE.    2.(y+1)dx+(4x−y)dy=0    Divided it by dx:    (y+1)+(4x−y)dydx=0    Transposed the (y+1)    (4x−y)dydx=−(y+1)    Divided it by (4x−y)    dydx=2y(x−3)    The farthest I can go is:    dxdy=(2x3x2)−(6y3x3).    The rest of the problems were easily solved but those 2 are very hard to bring to the standard form.

Josef Beil · Accepted Answer

for Nr. 2 is not linear, since it contain y*y

Kathryn Duggan · Accepted Answer

The second problem is given as  (y+1)dx+(4x−y)dy=0  if you divide by dy instead of dx then you will form  (y+1)dxdy=−4x+y  which simplifies to  dxdy=(−4y+1)x+yy+1  or  dxdy=f(y)x+g(y)  which is a first-order linear ordinary differential equation.  The sixth problem is given as  3xdxdy=2y(x−3)  where rearranging leads to  12ydy=x−33xdx  or  12ydy=(13−1x)dx  which can be solved by techniques which are known to you.

I was stuck at numbers 2 and 6. This is

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