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This is actually part of a larger problem of solving a diff EQ by use of a laplce transform, but it's the partial fraction part that I'm stuck on.

[tex]\frac{1}{s^2(s^2+w^2)} = \frac{A}{s}+\frac{B}{s^2}+\frac{C*s+D}{s^2+w^2}[/tex]

Good so far?

If I then multiply through by the common denominator I get

EQ.2[tex]1 = A*s(s^2+w^2) + B(s^2+w^2) + s^2(C*s+D)[/tex]

So then I set s=0

[tex]1=B*w^2 \longrightarrow B=1/w^2 [/tex]

Then using the quadratic equation, I find that the roots of s^2+w^2 are +/- jw

letting s=jw I end up with

[tex]1 = -jC*w^3 - Dw^2[/tex]

this is where I get stuck, I'm not sure how to find C and D at this point.

Note: I just noticed a mistake in EQ.2,

[tex]\frac{1}{s^2(s^2+w^2)} = \frac{A}{s}+\frac{B}{s^2}+\frac{C*s+D}{s^2+w^2}[/tex]

Good so far?

If I then multiply through by the common denominator I get

EQ.2[tex]1 = A*s(s^2+w^2) + B(s^2+w^2) + s^2(C*s+D)[/tex]

So then I set s=0

[tex]1=B*w^2 \longrightarrow B=1/w^2 [/tex]

Then using the quadratic equation, I find that the roots of s^2+w^2 are +/- jw

letting s=jw I end up with

[tex]1 = -jC*w^3 - Dw^2[/tex]

this is where I get stuck, I'm not sure how to find C and D at this point.

Note: I just noticed a mistake in EQ.2,

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