Second order linear differential equations

It is well known that a first order linear ordinary differential equation
x' +a(t)x=b(t) has a general solution expressible in terms of integrals
involving a and b.
But how about second order equation
x''+a(t)x'+b(t)x=c(t)
Do such formulae exist? If not, did anyone prove that such formulae do not
exist?
My belief is that such formulae do not exist, but no one has given this a
rigorous proof. Am I right?


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Relevant Pages

  • Re: Second order linear differential equations
    ... It is well known that a first order linear ordinary differential equation ... x' +ax=bhas a general solution expressible in terms of integrals ... No - If you add and subtract f.x', expressing the second order ...
    (sci.math)
  • Re: Second order linear differential equations
    ... It is well known that a first order linear ordinary differential equation ... x' +ax=bhas a general solution expressible in terms of integrals ... No - If you add and subtract f.x', expressing the second order ... two square-bracketed terms have the same integrating factor ...
    (sci.math)