°y''' +bx^y"-+ cxy' + ky = 0, where a, b, c, and k are constants. a third-order euler equation is one of the form ax if x> 0, then the substitution v = in x transforms the equation into the constant coefficient linear equation below, with independent variable v. dy + ky 0 dv y +(c b 2a) dv + (b - за)- dv a make the substitution v in x to find the general solution of 2x y"'9xy 5xy' 0 for x > 0. c, in x+cax y(x)c