Trap 1: Degree Not Defined If the DE contains sin(dy/dx), e^(dy/dx), ln(d^2y/dx^2), etc., the degree is NOT defined. Only polynomial expressions in derivatives have a degree.

Trap 2: Removing Radicals Changes Degree d^2y/dx^2 = sqrt(1 + (dy/dx)^2) has undefined degree as written. But squaring: (y'')^2 = 1 + (y')^2 gives degree 2. Always simplify before finding degree.

Trap 3: Confusing Order with Degree In (d^2y/dx^2)^3 + dy/dx = 0: order = 2 (from d^2y/dx^2), degree = 3 (power of highest derivative). These are independent concepts.

Trap 4: Linear vs Bernoulli Misidentification dy/dx + y = y^2 is Bernoulli (n=2), NOT linear. Linear requires the right side to be Q(x) only, not Q(x)*y^n.

Trap 5: Wrong Integrating Factor For dy/dx + Py = Q, IF = e^(integral P dx). Common error: using P = coefficient of y without first dividing the entire equation to make the coefficient of dy/dx equal to 1. Example: x*dy/dx + 2y = x^3 must be rewritten as dy/dx + 2y/x = x^2 before finding IF.

Trap 6: Homogeneity Check (x + y + 1)/(x - y + 2) is NOT homogeneous because of the constant terms +1 and +2. Translate the origin first to remove constants.

Trap 7: Missing Absolute Value in Separation When separating variables and integrating 1/y, write ln|y| not ln(y). The absolute value matters when the function can be negative.