Question

a.) Show that the DE is exact and find a general solution

2y - y^2sec^2(xy^2)+[2x-2xysec^2(xy^2)]y' = 0

b.) Verify that the equation is not exact. Multiply by integrating factor u(x, y) = x and show that resulting equation is exact, then find a general solution.

(3xy+y^2) + (x^2 + xy)dy/dx = 0

c.) Verify that the equation is not exact. Multiply by integrating factor u(x, y) = xy and show that resulting equation is exact, then find a general solution.

(-xysinx + 2y cosx) + 2xcosx(dy/dx) = 0

Answer 1

Here we use simple formula and methods,how to solve the above differential equation i.e method for exact differential equation and simply integrate.