Undetermined Coefficients:
a) y'' + y' - 2y = x^2
b) y'' + 4y = e^3x
c) y'' + y' - 2y = sin x
d) y" - 4y = xe^x + cos 2x
e) Determine the correct form of a particular solution, do not solve
y" + y = sin x
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....