Solving Diff. Equation: 2x+y-3 with Substitutions

[alseth]

hey, i have some problems with this diff. equation
dy/dx=(2x+y-3)^(1/2)
i tried to do some substitution
v=2x+y-3
then
dv/dx=2+dy/dx
dy/dx=dv/dx-2
then i substituted back into original equation
dv/dx-2=v^(1/2)
dv/(v^(1/2)+2)=dx
integrated and got something like this
2v^(1/2)-4ln(v^(1/2)+2)=x+c

i do not know whether this is the correct method and what to do with 2v^(1/2)-4ln(v^(1/2)+2)=x+c

thanks for the advice

 

[Dick]

Your solution looks just fine. About all you can do is put v=2x+y-3 back in. Sometimes you get solutions where you can't solve for y as a function of x in a closed form.