I'm not currently in a class, but I'm doing this for fun.. but technically I would still call it coursework, so I'm posting it here..

I'm studying Redheffer/Sokolnikoff's Mathmatics of Modern Engineering.. and I find a problem on page 75, use the method of variation of parameters to find the solution of this equation:

Y` + 3Y = X^3

this one is easy enough to find the forced response by plugging in

Y= AX^3 + BX^2 + CX + D = X^3, and equating the coefficients.

The coefficients turn out to be A=1/3, B=-1/3, C=-2/9, D=-2/27.

This is the answer, but that's not my problem.

The variation of parameter method discussed in this section requires two linearly independant solutions to the homogenous equation,, of which I can only find one:

Y= Ke^(-3t).

Of course there is the trivial solution, but that would make the Wronksian in the denominator of the integrals zero.

For the life of me, I can't see how in the world one can use the variation of parameters method to solve this..

Is it perhaps a trick question? I'd email Sokolnikoff.. but he's long since left the world..

any ideas?

I'm studying Redheffer/Sokolnikoff's Mathmatics of Modern Engineering.. and I find a problem on page 75, use the method of variation of parameters to find the solution of this equation:

Y` + 3Y = X^3

this one is easy enough to find the forced response by plugging in

Y= AX^3 + BX^2 + CX + D = X^3, and equating the coefficients.

The coefficients turn out to be A=1/3, B=-1/3, C=-2/9, D=-2/27.

This is the answer, but that's not my problem.

The variation of parameter method discussed in this section requires two linearly independant solutions to the homogenous equation,, of which I can only find one:

Y= Ke^(-3t).

Of course there is the trivial solution, but that would make the Wronksian in the denominator of the integrals zero.

For the life of me, I can't see how in the world one can use the variation of parameters method to solve this..

Is it perhaps a trick question? I'd email Sokolnikoff.. but he's long since left the world..

any ideas?

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