For the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d^2y}{dx^2}+4 \frac{dy}{dx}=sinx[/tex]

One root of the auxiliary equation is '0' meaning the particular integral for the right hand side is x(Asinx+Bcosx). But is there any formal proof for making this claim that for 0 as one root is it is x(Asinx+Bcosx) or 0 were the two roots, the PI would be x^2(Asinx+Bcosx)?

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# 2nd order differential equations with constant coeff. The Particular integrals.

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