Solve

9x^(2)+y-1=(4y-x)y^('),y(1)=0

. Find a cubic equation in

x

whose roots

b

the domain of the solution. Given that this cubic has only one real root (which you can qu learn by searching on "cubic solver"), decide whether the domain extends to

+\\\\infty

or to

-\\\\alpha

\ For what

b

is this exact? Solve it for that

b:ye^(2xy)+x+bxe^(2xy)y^(')=0

.\ Show that this is exact after multiplication by

xe^(x)

, and solve it:

(x+2)siny+xy^(')cosy=