- #1
Bipolarity
- 776
- 2
There are a few theorems in my DE book whose proofs I've been trying to find, without much luck:
1) Given an nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient, any IVP of this ODE has a unique solution over some interval I centered about the IVP.
2) Abel's Theorem for nth order linear homogenous ODE: Given an nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient, if [itex] \{y_{1},y_{2}...y_{n} \}[/itex] are all solutions to the ODE on some interval I, and they have derivatives up to order (n-1) on I, then their Wronskian is either 0 everywhere on I or nonzero everywhere on I.
3) Every nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient has a fundamental set.
In what textbook might I find a proof of these theorems? Thanks!
BiP
1) Given an nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient, any IVP of this ODE has a unique solution over some interval I centered about the IVP.
2) Abel's Theorem for nth order linear homogenous ODE: Given an nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient, if [itex] \{y_{1},y_{2}...y_{n} \}[/itex] are all solutions to the ODE on some interval I, and they have derivatives up to order (n-1) on I, then their Wronskian is either 0 everywhere on I or nonzero everywhere on I.
3) Every nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient has a fundamental set.
In what textbook might I find a proof of these theorems? Thanks!
BiP