Please answer with a solution. Thank You!
1) Given a differential equation
(1−2x2−2y)dy−(4x3+4xy)dx = 0. Is it an exact
equation? Justify your answer. Solve the equation.
2) Given a differential equation (y3 − y2
sinx − x)dx + (3xy2 + 2y cos x)dy = 0. Is it an exact
equation? Justify your answer. Solve the equation.
3) Solve the linear equation of order one: dy/dx + (1 + 2/x)y =
x-2ex
4) Solve the linear equation of order one: xdy/dx...