# Transform a vector DE into a set of scalar DEs [closed]

I have the vector equality:

{{a,b},{c,d}}.D[{x1[t],x2[t]},t]=={{e,f},{g,h}}.{u1[t],u2[t]}


I want to solve this using DSolve. How do I transform the above vector equality into a list of 2 scalar equalities (automatically):

{a*x1'[t]+b*x2'[t]==e*u1[t]+f*u2[t], c*x1'[t]+d*x2'[t]==g*u1[t]+h*u2[t]}


How do I do this? Thanks!

• Thread[] ought to work. Commented Aug 3, 2015 at 16:06
• @Guesswhoitis. Awesome, Thread[LHS==RHS] (pseudocode) worked! Commented Aug 3, 2015 at 16:10
• In recent versions of Mathematica, you do not have to transform the vector equation into a pair of scalar equations before using solving them. Thus DSolve[{{a, b}, {c, d}}.D[{x1[t], x2[t]}, t] == {{e, f}, {g, h}}.{u1[t], u2[t]}, {x1[t], x2[t]}, t] works just fine as is, whether with "abstract" functions u[t], u2[t] and symbolic coefficient matrices, or with specific functions and actual values in the coefficient matrices. Commented Aug 3, 2015 at 16:18
• @SjoerdC.deVries can you provide a link please? Commented Aug 4, 2015 at 6:48
• @chris It was rather difficult to find, but I believe I was alluding to this question. Commented Aug 4, 2015 at 10:36