1. The problem statement, all variables and given/known data One solution y1(t) of the differential equation is given a) Use the method of reductions of order to obtain a second solution y2(t) b) Compute the wronskian formed by y1(t) and y2(t) 2. Relevant equations (t + 1)^2y'' - 4(t+1)y' + 6y = 0 y1(t) = (t+1)^2 3. The attempt at a solution i assume that the second solutions is y1(t)*u(t) where u(t) is some function of t that statisfies the diff eq y2(t) = y1(t)*u(t) = (t+1)^2*u(t) y2(t)' = 2(t+1)*u(t) + (t+1)^2*u(t)' y2(t)'' = 2u(t) + 2(t+1)*u(t)' + 2(t+1)*u(t)' + (t+1)^2*u(t)'' or y2(t)'' = 2u(t) + 4(t+1)*u(t)' + (t+1)^2*u(t)'' I plug these into the eqaution and reduce and I wind up with (t+1)^4*u(t)'' = 0 I do a reduction of order through v(t) = u(t)' and v(t)' = u(t)'' and the equations becomes (t+1)^4*v(t)' = 0 Here is where I may be going wrong, I divide the (t+1)^4 and just have v(t)' = 0 which then becomes u(t) = C1t + C2 so y2(t) = y1(t)* C1t + C2] or y2(t) = C1*y1(t)*t + C2y1(t) C1 can be folded into complimentary solution constant, so I assign 1 to that. C2 can be zero since its a multiple of the first solution. My problem is the answer is wrong. The book has (t+1)^3, I checked both y1 and the books answer and they both work. So I am lost as to what I did wrong. I showed it to a couple of post docs and they got the answer I got. Any help is much appreciated.