Exercise2 :
Solve the ODE
i)
(dy)/(dx)+(xy)/(1+x^(2))=x\sqrt(y)
.
ii)
(dy)/(dx)+(y)/(x)=(y^(2))/(x^(2))
.
Exercise 3 :
Find the values of parameters for which the ODE
(ax^(2)y+y^(3))dx+((1)/(3)x^(3)+bxy^(2))dy=0
is exact, and then solve it in the case of those values of
a
and
b
.
Exercise 4 :
Show that the DE
(x^(2)+y^(2)+x)dx+ydy=0
is not exact but becomes exact when multiplied by the integrating factor
\mu (x,y)=(1)/(x^(2)+y^(2))
. Then solve the equation.