(1) Consider the differential equation d'y r1333? (E)3 +6(dI3)5 +313)? J.F . The degree of this equation is 5. and the order is 3. (2) An appropriate substitution to reduce the differential equation y' = f(x + 23:) to a separable equation is u = x + 2y. (3] The differential 110:}? + 3:) may be written in the form :tdy + x. (4) There are no choices for 110:) and rfx) such that the linear equation 3:" + p(x)y = rfx) may be expressed as a separable equation. (5) The equation xy' = y + W may be expressed as a homogeneous equation. (6] To solve the rst order linear equation xy + x 2y: x2 , you need to calculate the integral l1: I x zdx. ('1') When solving the rst order homogeneous equation 1' 2: - ;using the substitution at = ; the dEI'lV-'rlVE 2? 1s replaced by 11 + xix {111. (3) The differential equation d2]: 2 y dxz+ +(E) = may be solved using the substitutions (9) If yl (x) and y; (x) are solutions for a non linear second- order differential equation, then any linear combination of y1 (x) and y: {x} will also be a solution. (Ill) The characteristic equation for the second order linear equation y\" 16y = {l is given by 1112 16m = f}