# Reference book for linear differential equation in the light of linear algebra.

Usually in undergraduate course student is introduced to mechanical things of differential equation consisting of calculations,integrations,and different methods or tricks of solving the equations without mentioning why we do so.For example in case of linear differential equation with constant coefficients,we first solve the reduced equation to find a complementary function and then find a particular integral for the equation.We are only told that in this way you would get the solution but not told why we are doing it e.g. that $$F(D)$$ is a linear operator and we are first finding kernel space of the operator by computing the complementary function.These things include a basis knowledge of linear algebra which I have now.So I want to understand properly the linear algebra aspects behind the methods of differential equation solving especially linear ones.Can anyone suggest me some reference book where I can find the reasons behind what we are doing to solve a linear differential equation(in light of linear algebra).I want to look at differential equations analytically not mechanically.I have already seen Hirsch Smale book which discusses on it but it does not fully satisfy my purpose.

• what about the book by Lawrence Perko? Also, what exactly is it about Hirsch Smale's book which is not satisfactory? (btw are you referring to their first edition, or the new one with Devaney, because there's a big difference) Perhaps if we know about what specifically you're looking for, you'll get better recommendations Commented Sep 29, 2019 at 7:25
• take a look at Arnold's textbook
– user173262
Commented Sep 29, 2019 at 7:43
• Yes they are alright but I am looking for a purely linear algebra approach.Although these two books were also helpful for me. Commented Sep 29, 2019 at 10:07