Trap 1: Degree Not Defined If the DE contains sin$\frac{dy}{dx}$, e^$\frac{dy}{dx}$, 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 + $\frac{dy}{dx}$^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 $\frac{x + y + 1}{(x - y + 2)}$ 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.