Obtain the differential equation by eliminating the arbitrary constants: y=e-2x(Acos x+Bsin x)

Exercise 6.2 · Q20

y=e^{-2x}(A\cos x+B\sin x)

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$y=e^{-2x}(A\cos x+B\sin x)$ has characteristic roots $-2\pm i$ (real part $-2$ , imaginary part $1$ ), so the auxiliary equation is $(m+2)^2+1=0$ , i.e. $m^2+4m+5=0$ . Hence $y$ solves $\dfrac{d^2y}{dx^2}+4\dfrac{dy}{dx}+5 …

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Q.Obtain the differential equation by eliminating the arbitrary constants: $y=e^{-2x}(A\cos x+B\sin x)$

Concept understanding — Formation of a Differential Equation whose General Solution is Given

Q.Obtain the differential equation by eliminating the arbitrary constants: y=e−2x(Acos⁡x+Bsin⁡x)y=e^{-2x}(A\cos x+B\sin x)y=e−2x(Acosx+Bsinx)

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Q.Obtain the differential equation by eliminating the arbitrary constants: $y=e^{-2x}(A\cos x+B\sin x)$

Unlock everything free for 14 days